If the user is already a Raptr user, you can simply search for them and go to their Profile Page. Once there, you can click "Follow" on the right side.
If they are not yet a Raptr user, you can invite them! When you're at your profile you can click on the side bar labeled "People".
Once there, you can find on the right side of the page a section called "Invite Friends to Raptr". You can either send invites through Facebook and Twitter, or send a direct email to a friend.