First, know what you're looking for, and don't get distracted!
When I started looking, my reguirements were simple! Gotta be cheap! I only had $15K cash to play with, and didn't want to finance. That narrowed the market considerably. Realizing that a large percentage of what you pay for in most aircraft is cosmetic (paint, interior, hangar rash) I was prepared to accept virtually anything, as long as it was dependable and solid! After all, my goal was to fly my own aircraft; not make the cover of "Plane and Pilot"! I soon had a list of maybe a dozen aircraft that fit that category (web search for "Cessna 150", Trade-A-Plane, etc.). I started making phone calls, and eliminating prospects. It soon became apparent there were 3 kinds of sellers. The first was the obnoxious type! "You do everything my way, give me unrefundable money, and I might let you buy my plane!". Forget them! Then there was the "This is a great buy, regardless of the fact it hasn't flown in 20 years, and has missing parts that you can buy anywhere" types! Don't buy their problems! The third type is the only one I would ever buy a plane from. Up front and above board about everything (there are honest sellers out there). Eager to answer questions. Wants a fair price for his bird, but will negotiate small discrepancies.
I found 84G through Trade-A-Plane in mid-state New York. Tom was easy to talk to, and we actually struck up a friendship over the phone. He sent pictures of everything I asked about, and gave detailed answers to all questions. I even talked to his mechanic, who had been signing off the annual for several years. Tom was willing to let my mechanic do a pre-buy/annual, and would make good on needed repairs, if any.
I loaded up my flight bag and bought a one-way ticket to New York. Tom picked me up at the airport and drove me to the the field where his plane was tied down. We pulled a few panels, and I did a quick inspection on the aircraft myself (I've been around airplanes since 1968, and I'm a licensed mechanic since 1979). No surprises! Everything that was obviously wrong had been fully disclosed, with no downing discrepancies. We test flew the airplane and everything worked properly. By now, it was getting late, so Tom put me up for the night while I looked over the logs. Not perfect, but none are! Just a minor miscalculation of total time, carried forward since 1978. I paid the $14,500, got my receipt and bill of sale, and we left for the airport to fly back to Florida with my new toy!
I gotta tell you, that is the greatest feeling I have ever had (other than the birth of my 3 children). Flying my own plane home on a long cross country for the first time was glorious, and I wouldn't have missed it for two Cessna's! I stopped overnight in Virginia to visit my Daughter and Grandchildren, then left for home (after having a gascolator O-ring replaced). The rest of the trip was uneventful (except for the door-to-door smile I couldn't get off my face)!
Don't be bashful with the seller. Ask questions, and get answers. Discuss what's negotiable and what's not. Don't get on that airliner with any question unanswered. Trust your gut! If you get a bad feeling, it's probably a bad deal. Treat people the way you want to be treated, and expect the same in return. Honesty is non-negotiable!