"what is a compost...?" -lol! That's ok, I'm learning too - homeownership is an education!
Basically, compost is broken-down organic materials. People have been using their food wastes in this way for ages, but it's gaining popularity among the "save the environment" crowd because it does cut down on what goes into landfills. And
gardeners have tons of uses for it.
You can just make a huge pile in your yard, then wet it and turn it every few days. Like this:
http://thehotpotato.files.wordpress.com/2007/06/adam-about-to-turn-the-compost-pile.jpg
Or you can use bins or a tumbler, like these:
http://www.adekun.com/media/CompostBinMk2.jpg
http://www.greenfingers.com/superstore/product.asp?dept_id=200337&pf_id=LS2485D
http://www.compostingtoiletsystem.net/?p=73
The heat that the decomposition and microbes create gets concentrated and breaks larger particles down into tiny, fine bits of all-natural fertilizer.
You need 4 ingredients for good compost: carbon ("browns"), nitrogen ("greens"), water, and air.
Carbon comes from dried (dead) plant material (good use for the leaves you rake up in fall) and chemical free paper (among other things), and nitrogen comes from freshly clipped or not completely dried
plant matter (like veggie scraps from the kitchen and grass clippings). The carbon and nitrogen materials need to be in a somewhat specific ratio, or you'll just have a stinky pile of muck (but it will still work). We did about 60% carbon to about
40% nitrogen (if it starts to stink, we'll just add some more dried shredded leaves). Shred or chop your materials so that the particles are smaller to start with, and your compost will finish faster.
Then you add water so it's about as wet as a damp sponge (turn it while you're watering it to evenly wet the pile). And you turn it every day or two (either in a spinning barrel or with a pitchfork if you're using a bin or pile)
to add air, so the aerobic microbes can do their jobs.
Some people use worms, bat poo, chicken poo, and other stuff to speed up the process, but it's not necessary if your pile is large enough to generate good heat.
If you do all this, and refrain from adding to a batch while it's "working", it should look like this within a few months:
http://www.organic-compost-tumbler.com/images/finished-compost.jpg
More info on composting: