How do I add friends on my xbox?

OK, I'm a ps3 guy all my life, but I recently switched to xbox. I just bought the xbox with the 250gb hard-drive that came with the kinect bundle. I must say xbox is way better than ps3, glad I made the switch. My question is how do I send a friend request. I have a buddy that I'm trying to add. I send him the requests and he says he doesn't get it. When he sends me one I don't get it. What are we doing wrong? I do have a 12 month gold memborship thought I bought set up last weekend. So I am on xbox live. I do not have any friends yet as I just bought the xbox 4 days ago. Any ideas? We double and triple checked to make sure we typed our gamertags in right.