A lot of reasons for a new check ride is because of insurance issues. Yes, as long as you have your private pilots license, you can operate any aircraft up to 200HP (without high performance or complex ratings) but people won't just let you use their aircraft. If he handed you the keys, you went up without being familiar with the aircraft, the V-speeds, etc, and have an incident/accident, his hull insurance goes sky high.
As far as paperwork, they'll need a record usually of your drivers licence, your medical, your FAA card, and sometimes your insurance card JUST IN CASE...
As far as what to expect? Basically, a BFR-type review. There will usually be a ground test on questions right out of the aircraft's POH. You'll usually sit down and discuss V-speeds, the weight and balance info, and any quirks of the aircraft. Then you'll go out and fly. A check out usually involves:
-the standard 180 degree clearing turn
-steep turns
-slow flight
-power off/power on stalls
-Emergency procedures(usually engine out scenario)
-3 touch and goes/stop in goes.
These are usually the minimum. They are not hard, but if you don't fly for a while and go try to get checked out in a larger aircraft(like I did) and don't do so hot, you might have to make two flights for a checkout. So far, I've had to do two flights to get checked out in each aircraft I rent.
Something that I was reminded by another pilot friend of mine is a checkout is not a bad thing, its a great way of basically getting a tune up of your flying skills. They can offer tips and techniques that may improve your skills. Even if you have 1000+hrs, and even then, a check out is usually standard practice.
Don't get upset that you have to do this, everyone does it!