In a nutshell, you do a thorough prebuy inspection (with an engineer who knows the type well and who
you trust), do a flight and make sure everything works, knock the price down by anything that needs fixing, knock the price down by anything that might be a can of worms, check for any liens (CAA?) and then you hand over the money and fly it away.
Buy the best you can afford, and leave yourself a decent amount left over for suprises
You have to be fairly careful because a lot of sellers are selling because they "know something"... I saw an absolutely astounding in-your-face crook not long ago who was selling a PA28 which had not flown for years and was so corroded the oil was leaking out of the engine. Some mug will pay the £40k asking price eventually.
The advertised prices tend to be some 20-30% too high for a quick sale, but this varies according to type, rarity etc.