small muslin bags (ours were 8"x6"), or cheesecloth;
a small chicken (not frozen!) that will fit in your container with room to spare on all sides;
wine (cooking wine is fine, and some recipes use rubbing alcohol instead);
salt (we used kosher, but table salt is fine);
sodium carbonate (you can find this with pool/spa supplies, or occasionally in the laundry aisle labeled "washing soda");
and paper towels.
You should wear gloves when handling the salt/baking soda/sodium carbonate mixture, and always wash thoroughly after handling the chicken or changing the salt it's packed in.
If your chicken came with the neck or any internal organs, remove and discard them. Then wash the chicken well, both inside and out. Rinse it again with wine or alcohol. (This helps disinfect the bird, reducing the amount of bacteria that will grow on it.)
Dry the chicken completely, both inside and out. This is important: the drier your chicken is, the better and faster the mummification process will go.
You need enough to pack the inside of the chicken and surround it, outside, with a couple of inches of the mixture. We used a 1-cup measuring scoop as our unit, and we tripled the recipe for our initial packing. You will have to adjust for yourself depending on the size of your chicken and the number of times you need to change the natron.
The natron helps dry the body tissues quickly. And bacteria and fungi can't grow (well) when they're deprived of water, so they can't cause rot and decay. Gutting and dehydrating is the same process deer hunters use today to make venison jerky.
Fill muslin bags with natron, or use cheesecloth and twine to make little natron packets, and the stuff the inside of the chicken with them. (A system like this makes it much easier to change the natron in a week, but you could also just pack the inside of the chicken with loose natron.)
Put an inch or two of the natron mixture in the bottom of your plastic container. Use twine to make a sling that will help you lift the chicken out, later, and place the chicken on top of the twine and natron in the container.
Fill more muslin bags with natron and completely cover the chicken with them. Or, if you're not using muslin/cheesecloth, pour loose natron over the chicken. You want to make sure that your bird is completely surrounded on all sides by an inch or two of the mixture.
Put on the lid and set your chicken aside. (You may want to use SaranWrap or Press'n'Seal as an additional odor barrier. Or, of your container fits, you can put it under an aquarium or inside a second container.)
Wait a week, or until the natron becomes very damp. At that point, remove the chicken and change the natron inside the cavity and surrounding the bird. (The chicken may smell, so work fast.)
Keep checking the natron, and change it whenever it gets damp. It may take six weeks, changing the natron weekly, to dry your chicken out thoroughly. When it's dry, it shouldn't smell.
Once the chicken is dry, remove it from the mummification chamber. (If you packed it in loose natron, you'll need to brush off the salt. You may even have to use a damp paper towel. Keep your chicken as dry as possible.)
Congratulations! You have a mummy.
If you want to, you can make your mummy more elaborate.
You can coat the inside of your chicken with cooking oil or baby oil, and then sprinkle it with sweet-smelling spices such as cinnamon, allspice, nutmeg, or cloves.
You can use gauze strips and Elmer's glue to wrap your mummy. (The ancient Egyptians used resin, but that's a whole different project.) For extra authenticity, find some photos of Egyptian animal mummies (like the hawk mummy) and try to imitate the wrapping technique.
Once wrapped, you can paint your mummy. Use hieroglyphics or Egyptian designs. You could even make a cartonnage mummy case for your chicken mummy's final resting place.