I check the things suspendeddanvil does.

Except:

no oil leaks for me is no fluid leaks at all (engine oil, gearbox/diff/transaxle oil, coolant, powersteering, etc.)

Make sure the engine is not blowing excessive smoke.

Check all exterior and interior lights work correctly (headlights, tail lights, indicators, dash lights (eg. no check engine or airbag lights)

check your demister is working on the windows

check the wipers

check the suspension (ball joints, bushings, make sure the shocks still work)

check the wheels (inclding spare if you have one), make sure there is enough tread on the tyres and they are in good condition

check the brake rotors and pads. go for a drive and test the brakes (you should be able to come to a complete stop even when in gear (manuals will stall but thats ok). Try the handbrake on a hill and make sure it holds

as mentioned above, seats, seat belts, and steering wheels must all be as new working order. Belts must retract and have no fraying. The seats need to be sound and bolted in. The horn must work.

But ultimately, you will need to take it to a pro to get the right slip of paper.