Originally Posted by Ace_Club
When the posts are removed, you can remove them by using a chopstick or something similar to press down on them til they pop out.
Not all of them pop out, I have a keg where one post (I think the gas post) has a lip on the inside of it where the "fingers" of the poppet lock onto. Haven't quite figured out exactly how to fully disassemble it without possibly destroying the poppet valve, but I've been able to clean it fine.
Just take a good look at the inside of the post to see how the poppet is retained before trying to force it out. Most of them, like Ace_Club said, just push out.