UPDATE: since the release of iOS 10 this response no longer applies. Hopefully Firemonkey will find another way besides Facebook for iPhone/iPad users to add friends.
@sebush1912
Here is how to add friends to Game Center (GC):
Open your GC and tap on friends.
At the top left area you will see a + sign. Tap on that. (See first screenshot below)
A message window will open (see second screenshot below). Type the person's GC ID in the To: section. Then type a message to let that person know why you are sending them a friend request. Something like "need sims Freeplay neighbors" or "Play sims Freeplay" would be appropriate.
You will not get any confirmation that they received the message unless they accept your request.
I also added a screenshot of the request I sent you.