Don't forget - don't go alone. Bring along a friend who is familiar with bikes and can help you inspect your choice.
If you are going the used bike route, there are a number of acceptable sources, whether a dealership, auctions or classifieds.
Here are some cursory issues, but to insure you are getting the best bike for your buck, go over the bike with a fine tooth comb. A guide bought at the local bookstore or borrowed from your library will help you determine if what you find is a sale breaking issue or merely a price bargaining point.
If you find just the bike you are looking for from a private seller, begin by asking the seller some questions about the bike's current condition and history. Ask if it has been in a garage or out in the open weather. Has the owner driven it cross town or cross country. Are they the only owner? What is the mileage? How much are they selling it for and why? See if they can give you a listing of repairs and maintenance. All this information will give you an idea about the bike's condition.
Then meet the bike face to face. Do the unfun stuff first, like checking the plate with the registration, the odometer reading with the title, the repair and maintenance records. No use paying money to someone for a bike they don't own.
Look for wear and tear, and make sure it matches with the bike's stated mileage. If the footpeg looks significantly worn but the odometer is at 2,500 you might feel some questions are in order. Ask as well if you see overly new parts, dirty parts, etc. The new parts might indicate a crash, the dirty parts could be masking cracks or leaks.
Everything should be aligned...everything straight and nothing out of whack. If it is, ask why.
Then go over your little beauty in finer detail with list in hand. And don't forget a flashlight for viewing in those hard-to-see places. Once you have been over the inspection issues, take a test ride if the seller will allow it. This will give you an idea of whether you and the bike are a good fit. However don't be amazed if the seller balks at the test ride. Potential buyers riding off on a "test ride" never to return is not an uncommon experience. Try leaving your car with them, or see if they will take you for a ride on the back.
If things are still a go, but you want a qualified inspection, have a mechanic inspect the bike for electrical issues, spark plug performance and leaks. Once you think you have the bike of your dreams, negotiate a good price. While at the library getting that motorcycle buying guide, look for the National Automobile Dealers Association motorcycle appraisal guide to get a ballpark figure for the bike.