If you'd prefer to compost without worms, that's fine.
Here's what to do.
This process takes a couple of months because you have to wait for stuff to decay.
Start in an out-of-the-way place in your yard. Make a heap of table scraps (not dairy, fat, or meat, which will attract rodents and other critters.)
Add garden wastes such as grass clippings, leaves, or plant prunings. Avoid anything big or woody because it won' decompose quickly.
When your heap is about 3 feet tall, cover it with 2 inches of aged manure, which is available at garden centers.
Water the pile, cover it with black plastic, and let it cook. It will get very hot inside.
Turn it with a pitchfork about once a week so that everything "cooks" consistently. The more often you turn it, the faster it cooks. If it doesn't cook, add more manure.
Continue to feed your compost pile with garden wast, sawdust, manure, table scraps, coffee grounds, eggshells, and shredded paper every week.
Keep the soil moist but not wet. (If it starts to smell, it;s too wet.
To keep flies from laying eggs on them, be sure to cover scraps with soil. Also add more paper or yard scraps each week.
When composting without worms, your compost should be fully cooked and ready to use in about two months.