I compost the following:
fruit and veg peelings, cores, past its' edibility
shredded personal documents and receipts
grass cuttings
paper bags
leaves
teabags
ash from barbeque
prunings/dead headings
cut flowers
windfall fruit
bedding plants at end of summer/basket plants
yellow pages
pet hair
wood or paper based cat litter, only wet, not the faeces.
(urine is an excellent accelerant)
I must have got it right, because there is a massive colony of worms living inside our bin. They just got in by themselves, attracted by the rotting vegetation. When I dig out the stuff from the bottom of the bin, I try to separate the worms by hand and pop them back in the bin before the compost goes on the flowerbeds. (Not at all squeamish, but I do wear thin surgical type latex gloves, as salt from the sweat on your hands irritates the worms skin! The worms are at all stages of life from tiny to enormous, and most have a pale band around them indicating that they're breeding.
I stopped doing eggshells because of attracting rats, too. Now the bin has a base; the holes for drainage are big enough to let worms and other insects in and out, but not rodents in. Our council now collect all types of waste food, cooked or raw, inluding meat and bones, so shells go in there with stuff that takes ages to rot like citrus peel.
Cutting things up into small pieces, or using a garden shredder and layering wet and potentially slimy things like grass with dry shredded paper will speed up the whole process. The end result doesn't have to look like the shop-bought stuff, as long as it is crumbly with no unpleasant smell and no obviously unrotted material it is fine.