If you want to bury your pet at home, be sure to check local, county, or state ordinances to make sure this is legal. You may also consider a pet cemetery.
The International Association of Pet Cemeteries and Crematories has a directory of pet cemeteries on its website.
Many people choose to have their pet cremated. Some companies will pick up your pet's remains from the vet's office or from your home. They'll let you have time for a memorial service if you want. Your vet may have a service he uses. If not, contact your local or state government for guidance and regulations.