As other suggested, having a spotter is a good idea, and making sure you are comfortable with conditions is important.

Depending on how comfortable you feel, it might not be a bad idea to let somoene else look over the plane and do a second pre-flight check just to make sure you didn't forget or miss anything.

Once in the air, here are a few things I do with a new plane in the first few flights (depending on how things progress (and not always in this order)):

- first, trim for mid-throttle, hands off straight flight.

- full throttle, does the pitch trim change? More importantly, do you pick up any roll (wing warps)

- inverted straight flight. Note how much down elevator is required to keep it level.

- low speed flight up high, up to and including a few stalls, paying particular attention if it drops one wing most of the time.

- snap roll left and right, does it snap, and how violently

- power dives, prefereably with no other plane in the air. Start with a fairly flat dive, getting steaper and faster. Listen for any signs of surface flutter. In steapest (vertical, if I get that far this early in testing, usually not) dives note if plane has a tendancy to pull out or tuck.

Depending on the type of airplane, there are a handful of other things I might do, and I might leave some of those off, but that's a start (but far from "complete") for a typical sport-acrobatic plane. There's a whole art to trimming an acrobatic plane that I personally don't usually bother with, but doing some of those things can make a sport plane fly better. I don't fly pattern or SA, the guys who do will know more about the finer points of trimming. I fly combat, fine adjustments aren't nearly as worthwhile (and I left out the combat-specific testing and trimming I do).