1) See if your area allows the animal be disposed of through local trash disposal. They will provide details on proper packaging. If not, find out if burial of organic matter is legal in your vicinity.
2) If burial is legal, go down far enough to be sure that at least 24 inches of soil will be on top of the carcass. Choose the location carefully to prevent cutting of underground pipes or cables or any contamination of the water supply (the burial site must be located at least 200 feet from any groundwater well that is used to supply potable drinking water, and the carcass must not come into contact with surface or groundwater). Digsafe or other company tasked to help property owners be aware of underground utilities would be a good place to call before any digging begins.
3) Sprinkle lime (the kind you spread on your grass) over the carcass and back fill and then on top of the ground to help control the odor. To add additional safety, cover the top with large rocks (at least 5 to 10 pounds), or cover the spot with hardware cloth (not chicken wire) and anchor it in place. Mesh should be at least 1-inch weave and extend at least 1 foot beyond the size of the hole on each side.