You should be able to mail your application, the fee, and your passport to the PRC consulate nearest you that processes tourist visas - google it up. You'll also have to pay for return postage. You may have to provide an itinerary, flight and hotel info, etc. Typically it's a one entry 30-day visa (for an American it's approx. $200), but dacox is right that multiple-entry ones are available too. If you intend to visit a few times the best one to get is the 5-year multiple-entry one, but usually that's issued to business people and those with family ties to the PRC. You can also use an agent who, for a fee, will handle all your paperwork and processing. They may be able to get you a better visa, such as the multiple-entry one.
Key is not sending the application in too early or too late.