Instead of thinking of my compost heap as something like a doghouse or a junk pile, to me it's a neighboring community of right-thinking friends. Here's what I have to say about that community:
In other words, in this world where so many things don't go right, it's just great living next to a wholesome, hungry, happy, neighbor.
If you don't have much stuff to compost, maybe you don't need to build or buy a compost bin. Some folks just toss what little kitchen scraps they have onto their garden soil and eventually the scraps decompose and get worked into the soil. If kitchen scraps have been seasoned with animal products they may attract raccoons or other animals you don't necessarily want in your garden. In that case, you might just collect your vegetable matter until you have a pot full, then go bury it in a shallow hole or trench in your garden. Eventually the matter will become part of the garden soil. You can also compost in a pile lying on the ground without any structure at all. Just feed the pile the right stuff, keep it moist but not wet, and stir it up every week or so to aerate it.
On the left I've forked in seven double layers of alternating hay and manure. After depositing each double layer I soaked it with water. Occasionally I dig into it to see how things are going and I'm always impressed by the heat, in some places so hot I can't hold my hand there for long. The heat is caused by microbes doing their jobs of decomposing the heap.
The bin has three compartments because once decomposition slows down and there's less heat produced in Bin #1 I'll pitchfork the whole heap into the middle bin, placing straw that's been on the heap's outside -- and thus not getting "cooked" like straw inside the heap -- inside. Redoing the heap also aerates the whole thing.
Once the heap is reconstituted in Bin #2, a new heap of fresh straw and manure will be piled into the first bin. Eventually that entire routine will be repeated, moving both heaps to the right. At the end of that cycle, what comes out of Bin #3 will be high-quality, spongy, nutrient-rich, sweet-smell compost.
Some people say never add eggshells and others say they're OK. My opinion is that adding washed eggshells is fine, but if they are sticky with egg remnants, you're inviting animals to dig up your heap. Clean eggshells are little more than calcium carbonate, or limestone, so adding them to your heap is like adding lime, which most gardens need. With time the shells fracture and contribute to the soil's looseness, which is good.
Mostly people compost vegetables, fruits, leaves and grassblades. Don't add animal products (including bones), wood, plastic, metal, or weeds whose seeds or other reproductive parts such as rhizomes or tubers might survive the composting process. I personally stay away from paper because you never know what chemicals have been added in the form of inks, preservatives, or whatever.
Mainly, microorganisms break down plant matter into tiny fragments that improve garden soil when added to it. Also, nutrients are made available for your garden plants. There are many kinds of microorganisms that do your composting, and each stage of the composting process requires its own special microorganism community.
When you compost, basically you are managing a series of microorganism communities. This is important to keep in mind because microbes, like humans, are made of a good bit of protein. And protein is made of amino acids, and each molecule of amino acid has at its heart an atom of nitrogen. Therefore, every healthy compost heap must have enough nitrogen for the making of the bodies of the needed microorganisms. The correct ratio of nitrogen atoms to carbon atoms (the carbon being in the vegetable matter being composted.) is 25 to 30 atoms of carbon for each one atom of nitrogen.
So, grass clippings, fallen leaves and such provide a lot of carbon but by themselves usually they don't contain enough nitrogen to make really good compost. To convert your grass clippings or leaves to compost, then, you have to add extra nitrogen. Wonderful sources of nitrogen are manure and urine. If you can clean out a livestock stall where the hay has been mingled with manure and saturated with urine, that's great stuff! Mix it in with your grass clippings and you'll get perfect compost. If you don't have such fine stuff, store-bought nitrogen fertilizer bought in a bag will do, though that stuff is made using lots of energy, so you're sort of defeating the idea of doing something earthy. Some people mix bagged dogfood, which has animal parts in it and protein-rich soy meal, into their compost bins to serve as a nitrogen source.
You also need to inoculate your compost with microorganisms. You can buy inoculant at garden shops, or just find some rich soil where organic material has been decaying for a long time, dig up a shovelful, and add it to your heap.
You might enjoy reviewing a page at Mastercomposter.com called "How A Compost Pile Works."