Short version: Mother Nature never throws anything away.
Longer version: Composting is the rare silk purse from sow's ear, something for nothing, win-win. You start out with kitchen, yard and garden debris and wind up with two benefits: 1) a great soil amendment, and 2) many green points for avoiding the landfill.
It's easy to fall into thinking that compost's last name is bin, and that careful layering and turning are part of the deal. But piling shredded leaves in a corner counts too. So does "trench composting," handy for those with little garden space, and so does bringing your kitchen scraps to a place (try the nearest community garden) that will compost them if you can't. I have a friend in Manhattan, for instance, who brings her coffee grounds, orange peels and such to the Lower East Side Ecology Center at Union Square Greenmarket.
See the three simple steps to making compost.2. Use Compost
Spread it around plants to ward off disease; put a bit in your potting mix to add slow-release micronutrients; top-dress beds with it to improve soil structure no matter what kind of soil you have; use it to help restore life to soil that's exhausted from years of chemical abuse. Sprinkle it on the lawn spring and fall to encourage the shallow grass roots... It's almost impossible to use too much.3. Plant Crops in Wide Beds
Crops are anything planted for harvesting: vegetables, cutting flowers, shrubs on hold to be transplanted... keeping these grouped as tightly as possible in beds that are not trod upon cuts down on weeding, conserves water, allows the compost to be concentrated where it will do the most good and improves soil structure year upon year as the layers of organic matter pile up. These beds are frequently raised or at least corralled neatly by boards or — I saw it once and am still impressed all these years later — by long slabs of granite. Aesthetics aside, the primary virtue of this tidiness is easier path maintenance. From the soil and plant point of view it's the special treatment that matters.4. Mulch
Mulch clothes the soil in a protective barrier that moderates temperature, conserves water, helps keep soil-borne diseases from splashing up and helps keep soil itself from splashing up — on your lettuce, for instance. Almost any organic mulch that will rot down into the soil is almost always preferable to landscape fabric with some kind of icing, but choosing the right mulch for each job is worth the extra effort.
Straw for instance is inexpensive, but it's untidy compared to wood chips and it breaks down a lot faster. That suits straw to the vegetable patch while the chips win under shrubs. (The specialized mulches for warming soil and/or reflecting back just the right light upon your vegetables are seldom biodegradable. My experiments with them are ongoing so all I can say at this point is: Remember that they work only when light falls on them; the more your garden resembles a jungle — no names, please — the less effective they will