In many cases, gardeners will just toss piles of leaves, grass clippings, mulch, and old organic food waste into a pile and let time work its magic in breaking down and decomposing the matter. However, to speed up the process, you can utilize chipper shredders to break down and blend up the compost, effectively giving Mother Nature a little bit more down-time.
Just make sure to only use the chipper shredder for outdoor waste such as leaves, twigs, branches, logs, and dry grass clippings. Don't run kitchen scraps through your chipper shredder, as they're typically moist/sticky and contain bacteria.
When breaking down and mixing compost, it's best to use a 50-50 or 70-30 blend. That's 50% live matter (i.e. green vegetation, old bell peppers, lettuce, and anything else that's not dead and dried out) and 50% dry leaves, twigs, and mulch. Or for a "hotter" compost pile, use 70% live and 30% dried matter.
Using kitchen scraps is a great way to add to the variety of your compost heap, but make sure you don't use meats, cheeses, or old chicken bones. Those kinds of materials will rot and ruin your compost pile while adding unsafe and unwanted toxins to the mix.
Once you've got all of your organic compost broken down into smaller pieces and blended with your kitchen scraps, add whatever other minerals into it, stir it with a pitch fork or other similar tool, and leave it alone. Let nature run its coarse. Every now and then, stir your compost pile to release excess heat and moisture. If you leave it too long without stirring, the heat and moisture will turn your precious compost into a gooey mess instead of the nutrient-rich soil you're aiming for.
If you don't already have a chipper shredder for breaking down yard waste, there are many good models available as well as how-to guides and other helpful information that can be found at Chippers Direct online.