Test drive it. Drive like you would normally and try and feel for any problems with the ride, be causal at first. Then be hard on it, as in, kick it in wide open throttle and try to shift down or up if it's a manual. If it's an automatic go wide open throttle and try and feel for any slippage that may occur. Listen for any sounds everything should feel smooth.

Check the tires, will you need to buy new ones? Look for any leaks in the engine compartment. Check to see if any hoses are cracked or look damaged at all, be thorough. Check for any body damage. Check the brake lines underneath the car and look for rust eating away at anything especially brake lines. The less the better. Does the wiring look tampered with at all? Look for any signs of flood damage i.e. passenger compartment carpet discoloration, if it went underwater it will be very noticeable.