Here is how I invite a user to a game.

1) Go to that persons profile
2) Find the " Invite PLAYER to a game of ____", choose a game and hit send
3)This page you have lots of options to invite multiply games, who is what color, etc - default is 1 normal game. At this point, you should be able to hit Send.
4) At this point it is waiting for the other person to accept. on the bottom of your main page, you will see a list of invites you have sent.

If you are still having problems, let me know and I can try to help.