Hold the lens up to a light if you can look through it or with light reflecting from it if not and check for internal marks. If there are small lines that appear etched into the surface avoid at all cost. This lens has fungus and will affect the quality of pictures. If there are chips or scratches on the surface elements in the centre also avoid, but if they are around the edge you shouldn't see too much problems. The resale value will be reduced dramatically and it won't look good.
Make sure the mount of an interchangeable lens isn't worn badly. This will provide a sloppy fitting and could let light in.
Also make sure any connections from the lens to body are not damaged. Auto cameras have electronic contacts which should be free from marks and manual ones have a coupling pins that shouldn't be sprained.
If the camera has a manual focusing ring slowly rotate it from the closest setting to infinity making sure there are no points where it sticks are grates. If it does the mechanism will either be sprained or have grit in it. Ideally this would need taking apart, cleaning and reassembling.
Check that the autofocus works by pointing the camera at different subject distances and pressing the shutter to see how it reacts.
Many cameras have plastic, paint or leather coated surfaces. Treat cameras with badly scuffed surfaces with caution. The owner may not have looked after the camera and their may be less obvious damage.
If the covering is coming away from the body it can usually be stuck back down using adhesive. If you intend doing this check to make sure it hasn't shrunk.
Avoid scratched panels. It won't affect picture quality but will reduce the resale value and doesn't look as good. Try the camera set to various modes to see if the LCD digits are all okay.
Makes sure the camera you are buying has batteries that can A; be removed and B; still bought. Some older cameras took batteries that have now been discontinued and some even had non-user replaceable batteries which are costly to renew.
Look at the battery contacts in the battery compartment. If there is a green, brown or white deposit on the surface avoid. This is a sign that batteries have leaked and the damage could extend further.
If the camera has shutter speed control select each of the slower speeds and make sure you can see a difference between the settings. This will also highlight if the shutter is sticking open. Some cameras, notably early Canon SLRs from the A-series develop squeaky shutters. If the shutter has high pitch squeak avoid, it needs servicing which can be expensive. Olympus OM-10 and OM-20 had magnets to control the shutter, if they get dirty the shutter will stay open for longer than necessary, resulting in overexposure. Again the magnets can be cleaned, but this may be more expensive than the camera!
If the camera has a fully automatic shutter try covering the lens, or sensor and firing. Listen for two clicks, one to open and the second to close. The darker the ambient light the longer this will take.
If the camera is a single lens reflex open the back and check that the shutter blinds/blades are not sprained or worn.
Most cameras have a threaded tripod mount. Avoid if the thread is stripped.
If the camera has a built in flash fire it with a fresh set of batteries and see how long it takes to recharge. If it takes more than four or five seconds it could be at an end of its life.
If the camera has an accessory shoe where a flash can be attached slide one on and fire the shutter to see if the connections are okay. Avoid cameras with bent or cracked shoes.
Open the back of the camera and fire at a reflective surface with the flash on while looking through the lens. If it's all synchronising correctly you will see white through the lens when the shutter opens.
If the camera has a flash sync socket plug a flashgun in and check that that fires. If you don't intend using flash none of these points matter but once again make sure you get a reduction on the price of the camera as it will be harder to sell if you ever decide to.
Many cameras have a threaded ring at the front of the lens. This is used to attach filters and other lens accessories. You may find the mount dented or stripped of its thread. If you don't intend adding accessories this won't affect picture taking, but the resale value will drop considerably.
When you buy a used item ask for a guarantee of at least 90 days. If anything is wrong with the product this gives you time to check it out thoroughly and get it fixed or replaced for free if you find a fault.
This is really important when buying from a less knowledgeable source who may not have spotted any problems when the camera was traded in.
You may not need instructions on how to use your camera, but if you ever decide to sell it and the new buyer requires them, you'll increase the chance of selling it. Similarly the box and packaging mean a lot to some people so keep these safe too.