Humans create waste. It is endemic to how we live. The amount of waste we create can and should be minimized, but even the most aware folks can't eliminate waste entirely. How waste is disposed depends on the nature of the waste and the conditions in your area.
Fire: Burning trash is a time-honored method of disposal. Paper, cloth, and similar items can be easily burned, reducing their footprint to virtually nothing. Fire is also a historical method of disposal of contaminated items. Be careful burning plastics and other synthetic waste, however, as they can produce toxic fumes. Smoke from fires also give away your location, which is an important consideration if you want to avoid detection.
Compost: Plant material can be turned into useful compost.
- Store it in large, open bins or piles, away from dwellings.
- Add earthworms if they're available, and keep the pile moist.
- Turn or stir the pile weekly with a shovel or pitchfork.
- In time, it will begin to turn to a dark, rich soil that is wonderful on a garden.
- The compost will smell terrible during part of this process, thus the directive to keep it away from dwellings.
Storage/Burial: This is the least favorable of the disposal options. For off-grid living or short-duration emergencies, simply store your waste on site until a trip to a waste-disposal facility can be made. For longer term disposal, dig a trench deep enough that waste can be covered by roughly 2 feet of dirt. As the trench fills, extend an end and continue it in a line. Mark the location of your trench, so that you don't try and plant or build there.
Hopefully this helps. If anyone has any other innovative disposal methods, please share!