How could one go about biodegrading one's own waste?

By making as little waste as possible. That's really up there as a means of 'saving the planet', e. g. don't buy items with excessive packaging. This means, among other things, not putting your produce into a clear plastic bag and instead using a cloth bag for when you are taking it home. It also means using reusable shopping bags for all of your purchases, be they food or clothes. And not buying pre-made foods for the most part, and instead assembling the materials from scratch. Write to companies and tell them you would consider buying their products (and telling your friends to do so) if they used less packaging.

Hence I would say to start by simply reducing the waste you create.

Reuse, too. Get a jar with your spaghetti sauce? Then clean it thoroughly and use it instead of tupperware, or to store seashells from the beach or the like.

And recycle - glass jars, cans, and newspapers are recyclable all over the United States (I don't know which country you are in). Plastics are trickier but look at labels. Call your local government representative and find out what is recycled in your area, and why something isn't.

Then start worrying about biodegrading your own stuff. The first thing you want to do is, reduce the volume of it, as outlined above.