To invite your friends to be your neighbors, tap the Social tab which is the fourth button from the left at the bottom of the screen. This will open the Invite Friends section of the Social menu. Here, you can login to Facebook Connect, Openfeint, Apple Game Center, or simply invite your friends to be your neighbors by tapping on their portrait!
From this menu, you can also:
1) Check incoming messages which include received invites, challenges, and gifts