For an Online Chess game,
http://www.chess.com/echess/create_game
...if you know their username, you can enter it from the "Member" section when your creating a challenge.
You can also go to their profile page and click on "Challenge to Play":
If you want to challenge someone in Live Chess, go to the Games Tab; then the Players Tab. Find the member you want to challenge and click on "Play".
How do I play with a friend that i don't see in my list?