I'm trying to figure that out as well. I'm really into Last Stand: Dead Zone at the moment and looking to add some friendly survivors to my Friends List but the only way I've found to add anyone at all is to find their profile and friend request from there. The problem is that I have yet to discover how to search for individual player profiles.
I've had the same difficulty. I am wondering whether they want friend requests to only be people you already know from somewhere, to avoid the FB type thing.
Sorry for the double post, but I don't see any way to edit and update my previous post.
There is a how to add friends FAQ pinned to the top of this forum that was missed. It confirms that you can only add a friend from the user's profile and that there is no way to search. You have to know them already, though I imagine that you might be able to network through people to their friends for common interests, etc.