Okay, maybe I was a little strong in my original post - but my reading into Pilot16s post implied that he had probably not flown for some months and was probably not all that high-hours. If I'm incorrect in that, it clearly changes the position. Mind you I know the PA28 and C152 both pretty well, and would want to fly with an instructor if I'd been out of either for more than about 6 months.
As to single seaters, I've flown about half a dozen, none of which had a direct 2-seat equivalent that I could get checked out on. Firstly you (and the aeroplane owner) have to be realistically honest and happy about your flying ability ON THE DAY. Which means you are current on the nearest available other aeroplane that you could be, and have flown recently and often enough that you've spare capacity to think about the aeroplane. At the same time you need to be pretty intimate with the local geography, airfield procedures, etc - again you need to allow yourself as much spare mental capacity as possible.
Then you need a very thorough briefing from a pilot who knows it, making sure I had the salient points down on my kneeboard.
After a good long sit in, then some protracted taxiing to get a feel for the cockpit, I'd look to do a couple of practice rotations and low hops. Then, a conservative take-off (nothing clever) exactly by the book. Climb to a good safe height in some quiet airspace, and carefully feel around the envelope from stall to Vne, via sideslips, operation of services, simulated approaches, shallow then steep turns - getting a good feel for it (and not forgetting trimming for cruise as well!).
Then I'd come back, fly some very careful circuits, and finally sit down with somebody who knows the aeroplane and discuss the flight and what I'd learned - got right, got wrong.
This is how I've handled all my single-seat first flights bar one. That exception was a test flight on a museum piece where nobody had flown the type for about 10 years. Whilst I'd done a lot of homework about it's characteristics, I had no "expert pilot" to talk to, so had to be MUCH more careful. (But by jove it was satisfying!)
Even more care is needed of-course is the first flight of a new type, but I've not had that privilege yet - only of a few variants.
G