First, the event has to be currently active. Event distribution
still shows the last event Pokemon, even if the event is over. You
can't claim them, but it's still there for whatever reason. When an
event is going on, you have to fulfill the requirements to get the
event egg / Pokemon, and when you do, there will be a claim button
that shows up on the event distribution page. (Some events are
modified - the last event Pokemon egg claim was in emera square and
not the event distribution page.) Most past event Pokemon can be
bought in the event shop at the emera mall, but that requires event
points, which you can either buy with nuggets or randomly get from
mystery boxes with some luck.