Question: Should I buy some "compost additive" for my compost pile? What about some fertilizer or lime?
Answer: While it probably won't do any harm to stir in one of those secret-formula compost additives, they aren't necessary. You don't need lime or fertilizer either.
In truth, there are only five words to remember when making compost: brown, green, chopped, water and air. Mix brown (dead leaves or straw, for example) with green (grass clippings, vegetable trimmings), chop them up with a mower or shredder and add a little water. Toss it all together like a big stir-fry, and that's it.
You need much more brown than green, but there's plenty of leeway, so don't bother measuring exactly. You can make good compost with 1 part green stuff plus 10 to 25 parts brown stuff, as long as they're somewhat chopped and slightly moist. Get the mixture about as damp as a wrung-out sponge. Use a garden fork to fluff it when you make it, and again after about a week. Then just fluff it every time you add more stuff, mixing old and new as throughly as possible.
One exception, as far as "additives" go—animal manure will get the material to heat up and decompose faster. Just don't use dog or cat manure, which may contain pathogens. Stick to horse, cow, chicken or rabbit manure.
As for a fancy bin, all you really need is about 12 feet of sturdy wire fencing. Form it into a circle, joining the ends. To fluff and mix your compost, just lift the fence off and set it down a few feet away. Fork everything back into it. This will aerate the material thoroughly.