There are two types of timeshare rentals -- from the developer (Marriott, Hilton, Disney, Wyndham, etc) or from an individual timeshare owner, either directly or through a broker.
Rentals from the developer will be MUCH more expensive, and you book those on their website like any hotel reservation.
Rentals from an owner, or from an owner through a broker, should be quite a bit less expensive.
There are two websites where individual owners of many timeshares list their rentals -- Redweek and the Timeshare Users Group (TUG). Disney Vacation Club rentals are also listed on the DIS DVC Rent/Trade board.
In addition to the direct rentals from owners, there are a number of brokers who facilitate owner rentals. They might be a little more than a direct rental, but might also offer some additional protection to the consumer.
eBay also has timeshare rentals and those could be either directly from an owner or through a broker.