Just do the standard car check, like you would on any other car. It's not a hybrid where you have $5K battery replacement cost to worry about.
Biggest issues are ALWAYS body work, rust and collision damage - walk around and look underneath. Note any damage and consider how much it will cost to fix it ... and then multiply that figure by 10 ...it's always more than appears on the surface and labor cost WILL kill you.
For mechanical stuff - most can be fixed fairly easily, so I usually don't worry too much if it's brakes, or CV joints, or suspension that needs some work, or O2 sensor, or IACV/idling problem; however if you notice that a lot of things need fixing - that car was neglected and now it's a systemic problem - PASS.
For major mechanical stuff - just make sure that tranny is shifting well and for the engine - let it run for a few minutes at idle and then ask the seller to step on the gas while you look at the exhaust - note if you see a puff of smoke - means valve seals are worn. Also check for overheating and leaking head gasket.
And don't worry too much about minor stuff, any 15 year old car will need SOME work. When I buy an old car, I usually set aside ~1K for repairs and that covers me for 3-4 years.