Becoming a Foster is a relatively simple process. Start by completing an application, and then wait for one or more rescues to contact you. Or, if you know who you would like to volunteer for, simply fill out a foster application directly with that rescue.
Keep in mind that most rescues are volunteer-run and it may take a couple days before someone contacts you. The next step is usually verification of some information (references, vet information, landlord if any, etc.), possibly some training, and then a home visit by another rescue volunteer.
Once you are approved, the rescue will let you know how to find out about pets available to foster, and you will be off and running!