In a nutshell : very carefully.
I was lucky.
My deal is, I was going to purchase the rental 150 from the flight school I fly from, and work at. But about a week before the deal was going to be done, 97J got destroyed (I'm still ticked off about that!).
The same day I heard the news, I began hunting for a 67 model, particularly one that began with 3 and ended with J. 3997J. I found N3740J. In Gallipolis, OH. 5300 TT, 287 SMOH... sounds like a good deal for $19,000. Only a grand more than I would have paid for the 4200 TT 1,200 SMOH rental bird. Saw some pictures, looked good, called the guy up, the sheriff of Gallia County, OH. Sounded like a cool dude, asked some questions about the plane, decided it was a go. The same day a deposit for $1,000 was sent out.
3 weeks later, I was on a 1-way flight to the nearest commercial airport (a 45 min drive) and the Sheriff picked us up. I brought along a fellow line guy and commercial rated pilot to help out.
As soon as we rolled up to the airport the plane was as (she was away getting some radios done) I knew it was mine!
I inspected it, took the cowling off, looked in the nook and crannies, and she tasted good. Flew it back to it's home base, it flew well!
Asked to borrow the logs overnight, went through them , found she missed 2 annuals back in the 80s (even though it flew about 40 hours illegaly... oops!) Decided she was mine, called up the ATM (aka, my father) the money was wired and I was on my way. Besides some crummy (VFR) weather, the flight home was awesome and an adventure.
At home, the maint shop I work at did a post buy to see exactly what I got myself into... and luckily their opinion was the same as mine, a nice, tight bird.
That's the last time I will be that quick to buy and that trusting. Nothing bad came of it, and the aircraft is a good one, definately not a lemon (a Gremlin, yes, but not a lemon).
I was lucky with this one!!
But... it's the one I wanted, and it's the last one I want to own (meaning I don't need any other plane but this one!!)
Good luck!