For purposes of licensing and registration, Japanese motorcycles are classed in three sizes. The smallest is 50 cc, midsize is between 100 and 125 cc., and the largest is 250 cc and over. Motorcycles in the largest class are required to have safety certifications, called "shaken."
You must have a valid motorcycle license in your home country and an international driving permit to buy a motorcycle. In addition, you must register as a temporary resident in the town office where you are staying. You will receive an alien registration certificate, which the dealer needs to process the sales transaction.
You can buy a motorcycle for export from any dealer, who will process the customs forms and "shaken" for you. If you plan to drive it in Japan, you need to purchase insurance. Many companies offer policies only to holders of resident alien (gaijin) cards, but some will insure travelers. Your dealer will probably be able to help you find such a company.
Learn and obey the laws and speed limits if you drive in Japan. Police in all major cities conduct regular speed checks, and tickets are expensive. Wear a helmet at all times, and park only in designated parking spots. Parking tickets are just as expensive as speeding tickets, and illegally parked motorcycles are regularly impounded.
