You mean making them gain levels? Just post When they'll be ready to evolve, there will be a green arrow besides them in the Pokémon collection tab of your profile, click it to make them evolve. Here every Pokémon has an evolution by level. Look at the pinned Dex thread in the Safari Zone for all information we currently have about the mons here!
The way it works here is that it takes a certain amount of posts to level up your Pokémon. So basically you can train your Pokémon by being active around the forum and making posts.
Yup, just post around the forums! When you view your Pokémon buddy, the text below it should say "# posts to Level #." For most Pokémon it's just 3 posts per level, but higher evolutions and some unique Pokémon like legendaries take more posts per level. The only exception to this is the Game Corner section, since posts there do not add towards your post count.