First, actually inspect the bike with your own eyes. It is not a good idea to buy a used motorcycle over the Internet sight unseen.
Bring a friend. If you do not have your motorcycle license yet, bring a friend with a motorcycle license. Bring two helmets.
Sit on the bike with your hands on the handlebars. Sit for at least a few minutes. Is it comfortable? Does the riding position feel natural? How well can both feet touch the ground? Is the seat comfortable? A bike that doesn't fit well and is uncomfortable will not be very enjoyable to ride for any length of time. If you can not put both feet flat on the ground this may be a problem while stopped in traffic. If you have to lean over even slightly while stopped to hold the bike up you could easily lose your balance and drop the bike. This could be dangerous, or at the very least embarrassing.
Check some of the obvious items. It will give you an idea of how the bike was maintained.
Look at the chain. Is it rusty? Is it adjusted to near its limit? Do the sprockets look worn?
If it has adjustable brakes, are they adjusted to their limit? If it has disk brakes, are the disks rusty, pitted or grooved?
If the bike has a center stand, put it on the center stand. Have your friend hold the bike steady. Pull on the rear wheel from side to side. Is there any play in the swing arm?
Look at the tires. Is there good tread? Is there any weather checking?
Look at the oil. Does it look black and neglected or does it look like it had a recent change?
Look at the overall appearance. Is there lots of rust? Are pieces missing or broken? Are there any bad scratches or dents that you are unwilling to accept? Is the seat ripped?
Does the bike have excessive miles? Bikes from the south will tend to have more miles than bikes in the north because of the shorter riding season in the north. This is a judgment call depending where you live. It would not be unreasonable for a 25 year old motorcycle to have relatively high miles. This is not a problem as long as the bike appears well maintained.
Start the engine. Did the owner warm it up before you got there or was the engine cold? Was it easy to start? Did it turn over well or did the battery sound weak? Did it smoke when it started? Any unusual sounds? Is there excessive valve clatter?
Take it for a ride. How does the engine run? Does it smoke? Is there excessive valve train clatter? Are the muffler(s) in good condition? Does the transmission shift smoothly? Does the clutch slip? Are the brakes firm? Do the brakes squeal? Are there any unusual rattles? Does the suspension work well or easily bottom out?
Any defects you find are something that you may need to deal with in the future. Some items can be inexpensive to repair. However, some motorcycle parts can be surprisingly expensive. If it is an older bike, spare parts may not be readily available. Once you buy it, any repairs required to keep it on the road will be your responsibility.
It helps to know at what price bikes of similar size and age sell for in your local area. This will help you judge if the bike is priced correctly. Watch the classifieds.
If you decide to buy it, get yourself a maintenance manual. I got a Clymer manual for my bike on eBay for about $25. It will pay for itself the first time you use it. Even if you do not make your own repairs, you will understand your bike better and know what it needs when you bring it to the repair shop.
