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Stats are the basics of battling, there are only six types of stats in Pokémon.

Hit Points
Attack
Defense
Sp.Attack
Sp.Defense
Speed

All Pokémon stats have a formula, in PH the formula is almost exactly the same as in the real games:

Floor(((2*Base + IV + EV/4) * (Level / 100)) + Level + 10) (for HP)
Floor(((2*Base + IV + EV/4) * (Level / 100)) + 5 )*Nature*Item) (for ATK,DEF,SATK,SDEF,SPD)

Floor means round down no matter what (i.e, 274.83 = 274).
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As you may see, HP has a different formula to ensure Pokémon have more health than attack so battles are longer.
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In battle choosing “Attack,” uses your Pokémon's attack stat and the opponent's defense to calculate the damage output.
In battle choosing “Special attack,” attacks use your Pokémon's special attack stat and the opponent's special defense to calculate the damage output.
Whoever has more speed goes first and whoever gets to 0 HP from attacks faints, and must be switched out. Otherwise, you lose if everyone in your party/team fainted.
So you see, if you have more attack than special attack or vice versa, you should use those type of attacks. If they are both pretty much the same you should use which attack corresponds to the opponent's lowest stat (such as Blissey has a very low defense so you should use your attack moves instead of special attack moves) Because of how the equation works, Pokémon only reach their full potential at level 100+ so this is why stats seem to shift when you level up, and is also why EVs and IVs aren't as big of a deal when you are at a low level such as level 10.
Fun fact:Even though Shedninja is known to only have 1 health, in PH since there are no abilities Shedninja is able to have more than 1 health.

PH allows you to battle, even though it’s very different from the original games, it’s still very similar. In battle you have six buttons, two of those are the attack and special attack buttons were talked about previously in the Stats Section and use your attack and special attack stats. They can also be increased with type advantages and charging. There also is a chance for a hit to be critical which doubles the amount of damage you deal, the chance to get a critical hit can be increased via holding a dire hit. The type moves depend on what type your Pokémon is, for example, a ducklett will only be able to use water and flying moves because its type is water and flying.
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Blocking has a chance of blocking an attack to waste a turn, it has a chance of failing and is usually used to waste the opponent’s charged attack as charged attacks are only for one turn.
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Doing charge uses a turn to charge and make your attacks do more if you use them after charging. After one turn the charge turns off so it must be used the following turn you use it. It gives you the ability to super heal next turn. Contrary to popular belief, charges do not stack.
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Healing has a very high chance to fail and heals your health quite a bit, it is often recommended for stallers to use this. Without an item to increase it a pokemon can only use it 3 times.
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Super healing also has a chance of failing and heals your health full. Most stallers often use this when on low health. Without an item to increase it a pokemon can only use it 3 times. It can only be used if you're currently charged.

If you are a battler you might be quite familiar with this. Since there are no abilities these type advantages are final. Here is a type advantage chart:


1/2x means your attacks do half, 0x means your attacks have no effect, 2x means your attacks do double damage. Dual types cover more types such as ducklett water and flying types makes electric type moves do 4x more damage (electric beats flying and water), it is now immune to ground attacks, ice is now regular effective because it is water so now it only has two weaknesses. Type advantages can quickly turn the tide of a battle so remember to always use these first before sending out your Pokémon.

Effort values also known as EVs are values telling you how hard your pokemon trained. When getting a pokemon EVs are all at 0 and it is up to you to make them to 255, the max. In PH all 6 stats are capable of maxing at 255, and once they're maxed too 255 you get a warning from feeding them vitamins or massages saying they are at max already. EVs are very important if your pokemon are level 100 because 4 EVs equals 1 stat point, so you are capable of getting a 63 stat boost just by EV training your Pokémon! If they're not level 100 it’s very hard to find this value along with IVs. There are currently only 3 ways to increase your EVs, a low chance when interacting directly with a Pokémon, massages in the salon, and vitamins. Due to the nature of the equation, you can only find your EVs if your IVs are maxed out.

Individual values also known as IVs are values that can never be changed upon hatching, they are purely genetic. When getting a Pokémon, IVs can be at 0-31 for every 6 stats. In PH, all 6 stats are capable of maxing at 31, but there is a very low chance of getting to this. IVs aren’t as important but are still helpful to a pokemon. If your Pokémon is level 100 every 1 IV equals 1 stat point, so you are capable of getting a 31 stat boost at level 100 if you’re lucky enough to get exactly 31 IVs. If they're not level 100 it’s very hard to find this value along with EVs as previously mentioned. Currently, IV breeding isn't available in PH so getting a perfect IV Pokémon chance may even be higher than getting a shiny mega. Due to the nature of the equation, you can only find your IVs if you max out your EVs.

Base stats are the main source of your Pokémon’s stats. All Pokémon have different base stats, there are multiple sites to find your Pokémon’s base stat. For example, Ducklett’s base stats are
HP 62
Attack 44
Defense 50
Sp. Atk 44
Sp. Def 50
Speed 55
The base stats will always stay the same, but you should still use them to your advantage.
Fun Fact:Mega Pokémon work a little bit different than in the actual games-they give a 10% to all of your base stats except for HP! Which means Mega Charizard X & Y both have the same base stats along with Mega Mewtwo X & Y.

Natures are very simple and are labeled in a Pokémon’s page. There is no nature that can help or hinder HP, and there are some natures that do nothing at all. If they help they boost your stat by 10% (1.1 when doing math), if they hinder they lower your stat by 10% (0.9 when doing math). There are only 25 natures and 5 do nothing. Natures also determine which berry flavor your Pokémon likes, if a berry has multiple flavors and one of the flavors is liked, the Pokémon will eat it even if it also has a flavor the Pokémon dislikes. A good example is oran berries which since it has all the flavors every Pokémon likes it even though it always has the flavor they dislike if they dislike a flavor.

Leveling up is one of the most valuable assets of stat changes, without it you may never see your Pokémon’s true power! In here Pokémon over level 100 have the same stats as Pokémon level 100. Leveling up can higher stats and a lot of pokemon need to level up to evolve. Just like Egg groups, there are 6 types of exp groups Pokémon fall into.
Erratic (600,000 to level 100)
Fast (800,000 to level 100)
Medium Fast (1,000,000 to level 100)
Medium Slow (1,059,865 to level 100)
Slow (1,250,000 to level 100)
Fluctuating (1,640,000 to level 100)

In the real games, competitive Pokémon generally have types according to what they're best at. These names are non-official but are commonly used by people in battling.
Balanced/Mixed Sweeper: All stats are fairly balanced (HP= ATK= SPATK= DEF= SPDEF= SPD=). Just your good ordinary Pokémon you have always known, great for any situation and scanning an opponent's Pokémon. Generally, you should have at least 1-3 on your team.
Glass Cannon/Sweeper/Wall Breaker: Very high attack or special attack with some speed to sweep your opponent, known to be very fragile (HP-- ATK++ SPATK++ DEF-- SPDEF-- SPD++). Because of being known to be very good attacking wise, it is a wise idea to at least put 1-2 on your team. You shouldn't put a lot of these types of Pokémon as they faint rather quickly. Most glass cannons don't specialize in both physical and special attacks so remember to concentrate in only one attacking stat. Remember: Never, ever, higher their attack to just lower their speed with a power item. If you are going for a power anklet for your sweeper, its fine. Otherwise, you should just use the X items.
Tank: Have above average defense, special defense, hp, and decent attacking stats to slowly faint a Pokémon (HP+ ATK+/- SPATK+/- DEF+ SPDEF+ SPD--). Unlike glass cannons, you usually want to specialize them into being a special attacking tank or a regular one while keeping their defenses up. Like glass cannons though, you should at least have 1-2 Pokémon on your team that specialize in being tanks, one for special and one for physical. If you've read the glass cannons section I suggested to give only X items and power anklets, for tanks, I suggest to give anything other than power anklets.
Wall: Very high defense or/and special defense to stall opponents with usually a lot of HP also (HP++ ATK-- SPATK-- DEF++ SPDEF++ SPD--). Other stats are usually very low because of this. In the actual games they are mostly meant for stalling with moves such as toxic and stealth rocks, but in PH people usually use them to get chunks of opponent's health without fainting when they have a type advantage. People often don't use them because of better alternatives such as tanks here, but pokemon such as shuckle and mega steelix have been known to put up a fight. Similar to tanks though, you don't want to sacrifice their defenses so give them anything other than power anklets.

++ really good/above average (HP is above 438 for a level 100 Pokémon, 333 for all other stats)
+ above average
= average (HP is 254-290 for a level 100 Pokémon, for all other stats the average is 149-185)
- below average
-- really bad/below average (HP is below 192 for a level 100 Pokémon, for all other stats its 87)

Smogon Tiers
Smogon tiers are unofficial tier names for Pokémon but are still the most common thing used in competitive battling. Due to PH's lack of abilities and items this'll generally be different from Smogon's list and will most often never ban any Pokémon which is why most of the ban lists are removed and will only be in Uber.
Uber:Uber doesn't mean anything but is a banlist for almost all Pokémon. Sometimes Pokémon from here are allowed in matches, but generally. Most people will say things like 'No Ubers' or 'No Legends'. It usually contains legendaries and Pokémon with relatively high stats such as Mega Metagross.
OU:OU means "OverUsed". Pokémon from here are extremely common competitively and aren't banned. If they fall further they go into UU.
UU:UU means "UnderUsed". Pokémon from here are still considered usable but aren't used enough. If they fall further they go into RU. You may see these time to time though.
RU:RU means "Rarely Used". Pokémon from here are still considered usable but aren't used enough. If they fall further they go into NU. These are usually the Pokémon you see and you think, 'why didn't I think of that' such as zen Darmanitan!
NU:NU means "NeverUsed," and holds mostly Pokémon that aren't fully evolved or are bad competitively, if Pokémon from this tier aren't used enough they fall to PU tier. It doesn't literally mean never used, but it's pretty close. You may see them very very rarely though and when they do it will most likely do pretty bad like kricketune.
PU:PU doesn't mean anything and generally holds mostly Pokémon that aren't fully evolved and/or are bad competitively and aren't used enough in NeverUsed. Most of the time you may never even see these Pokémon at all, think of maractus. Pokémon here are generally not as competitive as other Pokémon.
LC:LC means "Little Cup" and holds Pokémon that aren't fit for battling and aren't fully evolved. Sometimes people like to host little cups for fun, but 2nd evolution Pokémon such as Porygon 2 usually dominate little cups.

Having the chance to boost a EV directly when interacting with a Pokémon seems to be only 1 EV for the stat and isn't highly recommended
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Salon data,
Natural Oil:5EVs for one random stat (LMC)
Strong Massage: 5 EVs for Attack (LMC)
Special Strong Massage: 5 EVs for Special Attack (LMC)
Body Massage: 5 EVs for Defense (LMC)
Special Body Massage: 5 EVs for Special Defense (LMC)
Limbs Massage: 5 EVs for Speed (LMC)
Flavour and Bath Massage:10 EVs for all stats (LMC)
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In the battle shop there are some items that can help you in battle when bought with BP, which is rewarded to you when you finish a battle on how good you did, here are the data for the items that give you a boost.
Leftovers: 5 healing limit except for 3 (LMC)
Big root: 5 super healing limit except for 3 (LMC)
Rare Candy: 1 level, resets exp
HP Up:10 HP EVs (LMC)
Protein: 10 Attack EVs (LMC)
Calcium: 10 Special Attack EVs (LMC)
Iron: 10 Special Defense Evs (LMC)
Zinc : 10 Special Defense Evs (LMC)
Carbos: 10 Speed Evs (LMC)
Dire hit: 1/2 critical hit except for 1/24 (NC)
X Attack:10% Attack (LMC)
X Special Attack:10% Special Attack (LMC)
X Defense:10% Defense (LMC)
X Special Defense:10% Special Defense (LMC)
X Speed:10% Speed (LMC)
X Attack 2:20% Attack (LMC)
X Special Attack 2:20% Special Attack (LMC)
X Defense 2:20% Defense (LMC)
X Special Defense 2:20% Special Defense (LMC)
X Speed 2:20% Speed (LMC)
Power Weight:50% HP, speed is halved (NC)
Power Bracer:50% Attack, speed is halved (NC)
Power Lens:50% Special Attack, speed is halved (NC)
Power Belt:50% Defense, Speed is halved (NC)
Power Band:50% Special Defense, speed is halved (NC)
Power Anklet:200% Speed, defense and special defense is halved.(NC)

NC=Needs Checking, data was assumed.
LMC=Little more checking, the data seems to be correct but I wouldn't say it is confirmed yet.
Anything else without it such as rare candy have no proof/data against it.