Closest you can do to this is to self freeze your account, in which you won't be able to play the site. Otherwise there's no such thing as private profiles.
Best you can do is not post up any info and remove the friend and messages buttons as well as comments but know even with those removed people CAN get around them. There is also in preferences (I think its there) where you can "hide" things like last seen online, birthday icon, and gifts from non friends. Though this is a pretty social site so I'd consider if being here is something that fits you.
FINALLY GOT THE 15K WARDROBE DONE!!!!! Next up gutting and selling it.