Keep safety in mind. Wear gloves and a mask to protect yourself as you get rid of the animal. You should also plan on changing out of your clothes outside and washing them thoroughly in hot water and bleach.
Use your nose to find the dead animal. It's disgusting, but that's your best tool. Sniff against the walls, in the ducts and up in the attic to locate the strongest source of the smell. You can also drill sniff holes in walls, if you know the smell is coming from a wall. While this is disgusting, you may be able to locate the dead animal and cut it out of your walls with minimal damage to your home.
Dig through insulation in your attic if you know the dead animal is in there.
Be prepared to climb everywhere. You may end up needing to go into attics, into crawlspaces or in basements to get to the dead animal. If you're claustrophobic, you may want to hire someone to remove the dead animal.
Plan on decontaminating the area with a cleaner such as OdorXit once you've removed the dead animal. This will help prevent the spread of any parasites and help get rid of the smell.
Check to make sure no more animals can get within your walls. Close up any holes or talk to a professional contractor or you may end up having to remove other dead animals.