Any healthy, seed free plant material can go in the compost pile. You can also include grass clippings, if you don’t treat your lawn with herbicides. Adding vegetable scraps and eggshells will speed up the process of turning compost into fertile garden soil material, and adding well rotted manure will too. Layering plant material with a matter rich in nitrogen in 6″ layers will provide the optimal compost pile.
Unfortunately, the entire process doesn’t smell or look good, so you might consider a closed system with a wheel so that you can turn the compost without stirring up the smell. These systems are designed to speed up the process too, so you get compost sooner. Also, be courteous to your neighbors and place the system in a remote enough location where it won’t bother anybody.