Many local pubs and restaurants also have notice boards where you might find relevant information on rentals. The Compass Magazine has a classified section that is very helpful as well.
Then of course, you can always go to a local real estate agent and enquire about rentals, but be prepared to pay for their services, depending on the circumstances, it can be either a standard fixed fee, or a percentage of your rental. Some agents only charge the landlords, some charge both. Make sure you ask beforehand.
Most landlords ask that you sign a contract, and you may need your Alien Registration Card and your passport. Some landlords may ask that a local person be your "guarantor". Make sure you have a Chinese speaking friend available to help "smooth" the process and help with communication problems. Contracts are usually signed on a yearly basis, though you could specify for shorter or longer terms depending on your needs, just be sure to communicate this with your landlord.
It is normal for the landlord to ask for one or two months' rental as a deposit. This is usually returned to you when you vacate the property, or would used as compensation should there be any serious damage to the property. Parking spaces are often available for rent as well (both for cars and scooters), but they do not necessarily come with the property. It is best to ask about this, and the rental is usually separate from the property rental.
If you rent an apartment, make sure you ask if the "management fee" is included in the rent. Management fees could be a few hundred dollars or up to a few thousand dollars depending on the size of the apartment and the amenities available. The rent may be cheap monthly, but the extra cost of the management fee may often not be mentioned when negotiating.