The adoption process may vary depending on the specific humane society, but in general, you find a pet you want to adopt and then fill out an application. You then meet with a staff member to decide if the pet is a good match for you and pay a fee.
You can find a pet in several ways. Many humane societies list their available pets for adoption on their own websites, or you can use a large pet adoption site such as Petfinder.com to search for listings. You can also visit the shelter in person, although it is a good idea to call ahead and make sure the shelter can accommodate you before going.
The application you fill out generally requires you to prove your identity and asks about your experience with pets. It also asks about any other pets you own. If it is approved, you generally go to meet the pet in person next. This may happen in an exercise yard or a special room. Many humane societies require all members of the family, sometimes including other pets, to meet the new animal before finalizing the adoption.
If that process goes well, you sign an adoption contract and pay the adoption fee. If your pet has completed all necessary medical care, you can generally take it home immediately. Some pets may need to be held a few days to complete basic procedures such as vaccination or spaying and neutering.