For my association (strongest corp on my server for 1 year now) : people send a message to the chairperson if they are interested in joining us. Then, the chair discusses with them, and if they are in agreement over the conditions (common goals, communication and motivation are the 3 key-points for my chair for example), then we might recruit.
We have founded the association almost 2 years ago, and it took 3 servers for us to get all the key-members, and over the past year, We've recruited 5-7 people that became key-members as well. 3-4 people joined this round, but they probably won't stick around.
The thing is, my chairperson is doing an amazing (and tiring !) job of "interviewing" candidates. And then, you have to have some luck as well (sometimes the association is full, and even though you could be a great addition, there is just no space anymore).
IMO, the easiest time to get into a big corp is right before EG (they already know who isn't gonna continue) or just after restart (some people don't show up). And of course, write to the chair and discuss with him/her.