1st thing is to look for is frame damage. If its a steel bike, it will usually bend from a hard crash, not break. Look at the bike from the side and check to see if the forks are bent back. a straight line through the head tube should run straight down the middle of the upper 1/3 of the blades of the fork. (The upper 1/3 (approximately) is the part of the fork before the fork curves forward.)
Next, check the intersection of the tubes attaching to the head tube for any wrinkles, kinks or cracks. Look especially at the bottom of the down tube, thats where the majority of the forces are concentrated in a crash. Check all the connections between tubes for cracks or kinks.
Check the rear dropouts for cracks.
Aluminum tends to crack, rather than bend. Look at the same areas as above for cracks.
Ride the bike and see if it rides fairly straight, not pulling. See if you can ride with no hands, if you can't, probably something wrong. Go through all the gears, check the brakes.
Check the bearings in the hubs, bottom bracket and pedals for stiffness, loose can be fixed easily, stiff is usually more serious.
Lift the front wheel slightly and turn the bars. If you feel a notch and catch at dead center, the headset needs to be replaced.
Spin the wheel and look at a brake pad for reference (or the fork) to get an idea of true, same for the rear. Check the tension of spokes by squeezing two adjacent spokes, they should feel very tight. If they feel like guitar strings, no go.. On the front, the tension should be the same on both side of the wheel. On the rear, the freewheel side spokes will be very, very tight, on the other side, you will feel less tension but still tight.
Il faut de l'audace, encore de l'audace, toujours de l'audace
1980 3Rensho-- 1975 Raleigh Sprite 3spd
1990s Raleigh M20 MTB--2007 Windsor Hour (track)
1988 Ducati 750 F1