how to add apps facebook to my page?

[say what]

I'm kinda new to facebook, and got an invite to play mafia guns, on my notifications it says that I might have received new gift ... how do you play that ...


anyways, I'm trying to undesrand how applications work. I also signed up for farmville and sudoku, how can I add it to my page...? I'v e seenprofiles where they have those added on their page .....? is that a badge? what is a badge? how can I send requests to my ffriends to play... how do apps work?
when I got o application page, I click on add to page.. but where it says which page.... it says no page found... ????