Hamster's can be wonderful, adorable pets--but they don't live forever. And when the time finally comes to see your pet off into the afterlife, there are certain bases that must be covered.
Don a good pair of rubber, latex or waterproof gloves--dishwashing gloves can work.
Double bag your hamster in two sturdy (for example, zipped top plastic) bags.
Wash the hamster's cage and accessories (hamster wheel, water bottle) in hot, soapy water. Then rinse the cage in one part bleach, nine parts water. Follow that with a wash of 70% alcohol solution, to reduce the corrosive action of the bleach. Place the litter in a plastic bag, preferably while wearing a mask.
Bury the hamster in an out-of-the-way plot, at least three feet deep, to ensure that it won't be unearthed by other animals. Alternatively, dispose of the hamster in the garbage. Be sure your local zoning laws allow this type of burial.
Remove your gloves and wash your hands thoroughly with soap or disinfectant. Carefully disinfect any other body parts that have come into contact with the hamster or its accessories.
You can reuse the cage to house another animal: consult your local pet store beforehand.