You can send them a friend request, and they have the chance to add you to their friend list. Likewise if they send you a friend request, you have the chance to add them to yours. You can't just type somebody's name, to add them to your friend list, they (or you) have to agree to the add !!
If you click on a person's name, it'll take you to their profile page, where you can send a friend request to them, but be patient as it may take a couple of days for them to respond. Hope this has been some help !!
Grateful thanks to PupsiK for the awesome sigs !!