For most catches, a single post's worth of battling will be enough to catch it. Rarer finds may require some chasing or tactical thinking to pursue the Pokémon, which can be spread out over multiple posts if one wishes. (Although if a multiple-post event takes place, I'm inclined to think posts would be spaced out to allow others to react [or act themselves] if they want to.) There are no special mechanics involved, though. No sense in making things too complicated.

Should I write up a post where Alix catches something, as an example of the basics?