Firstly, there are a number of great books out there on compost. Visit your local library or search the Internet if you want some good advice. The book I liked the most was "The Complete Compost Gardening Guide" by Barbara Pleasant and Deborah L. Martin. Initially I got a copy from the library, but then decided to invest and bought my own copy.
Composting is not complicated, but it's not just a matter of throwing food waste together and watching it turn to soil. As a matter of fact, I learned that lesson by trying just that. I had a rubbermaid tub on the balcony of a condo we lived in and just tossed our kitchen waste into it (I was so sick and tired of throwing all that organic material into a garbage bag). What I got was a sludgy mess that smelled rather like vomit. That's not compost! It was gross, so we decided to try the worm composting thing. And it did work ... for a while. Until maggots got into it. And then the worms moved to a friend's outdoor compost bin.
The composting experiment was on hold until we bought our first house and had some dirt of our own. The house also came with a black plastic composter, so we immediately started to collect our kitchen waste and put it in the composter. But one small black plastic composter wasn't enough for a property with some substantial leaf-producing trees, so three summers ago my Dad and I threw together a wooden compost bin with two square halves. Now we used both the plastic and the wooden one. In general, I use the black composter to put the fresh kitchen scraps in. Generally the kitchen stuff is wet and tends to smell after a while. So the first half of the wooden bin is used to mix leaves and the smelly stuff from the black bin. The other half of the wooden bin is used to "cure" the compost. To let it finish, really. I'm still new at it, but stuff rots and I've gotten some good compost. We moved the composter last fall, however, so it screwed up my system and we didn't have complete compost to put into the garden this spring. The partially composted material is good for mulch, though.
Okay, so here are some basics. There are items you put into your compost that are high in carbon (leaves, paper, cardboard, sawdust) and items that have more nitrogen (kitchen waste, manure). It kind of goes along the lines of wet stuff and dry stuff. Too much wet, nitrogren-rich material and you get an anaerobic, smelly pile leaning toward my vomit-tinted rubbermaid bucket. Too much dry, carbon-rich material and you'll have the same pile of leaves you started with in the fall. So layering kitchen waste with leaves, shreded newspaper or straw can really help your pile.
So what to put into your compost? Well, the general belief is that you can put pretty much all organic materials from your kitchen and garden into yout composter. Meat and dairy are discouraged because they tend to smell more and attract scavengers. I do, however, put dairy, some meat and the occasional set of chicken bones from soup into our composter (along with the occasional bird carcass that my cat has brought home - if I get to it before she does. Lately I've just been letting her eat them). The bones are good for the soil, but will take a really long time to decompose. I don't mind having chicken bones in my garden. If it bothers you, leave them out. Egg shells are great. They add calcium to the ground. The more crunched up the better. Coffee grounds, hair, and floor sweepings can all go in the compost, too. Sticks are a pain. Try to avoid putting them in unless you cut them up small. And avoid too many things like nut shells. I do put pistachio shells in sometimes, but they won't break down and will be chunky. Avacado pits are the same. DON'T put weeds in. You can, if you have a really hot compost pile, but in general you're just inviting more weeds into your garden.
Turning your compost pile is necessary. And it's hard work. And it's not fun (for me, anyhow), but you HAVE to do it if you want any success. One year I just took off my shoes and socks, rolled up my pants and just mucked around with my hands. But a garden fork works well (bare feet and garden fork are contra-indicated, by the way!). So if you're going to have a compost, get a small shovel and garden fork.
The composter has to be on the ground - not on concrete or gravel. We put ours on a gravel pad, but made sure that we dug through the gravel to the dirt in the centre of each bin. The little creepy crawlies and bugs in the ground are going to be your composting soldiers. They do the work. So don't make it too hard for them.
When you start your compost, mix some soil in with it. It will help the process start. There are compost starters you can buy, but I've never done that, and our pile is working out just fine. And I like to cover my compost pile with a layer of newspaper that is held down by pieces of scrap lumber. It helps keep the heat in (yes, if you're doing it right, there will be heat) and the moisture, too. You could used old carpet or cardboard, too.
If the pile gets too dry, add water. If it gets too wet, shred newspapers and stir them in.
That's about all I can think of. If you have any questions, feel free to comment and I'll try to answer them. Otherwise, check out some of the great books people have written. They get very detailed.