Hi whip,
After you accept a game invite it should automatically load the game window and take you to the multiplayer lobby with the person who invited you. You can also receive friend invites through the invites tab as well, in which case after accepting you will just be added to each others friends list.
If you are accepting an invite from the website and a new window doesn't pop-up you may need to add an exception in your pop-up blocker settings. You can learn how to do that by clicking here.