Before you turn the key
Come when the engine is cold — a cold start is the most honest thing a used car does. Look under it for fresh drips, check the tires for even wear (uneven wear whispers about alignment or suspension), and open everything: doors, trunk, hood, fuel door. Check that the VIN on the dash matches the title and the ad.
The cold start
Listen for long cranking, rattles that fade as it warms, or smoke on startup. Watch the dash: every warning light should come on with the key and then go OFF. A check-engine light that never illuminates at all can mean the bulb was pulled — that's a walk-away sign.
On the road
• Brake firmly once from speed on an empty stretch — pulling, pulsing, or grinding is money.
• Let the wheel go light-handed on a straight road: the car should track straight.
• Take a highway ramp — listen for wheel-bearing hum and feel for shudder on acceleration.
• Work everything electric: windows, locks, seats, cameras, climate on both hot and cold.
Then let a pro finish it
If the car passes your fifteen minutes, a pre-purchase inspection at an independent shop settles the rest. A seller who won't allow one has answered your question a different way.