The microorganisms that break down organic material in your soil will happily do the same job in a compost bin. Your role as a composter is to provide the conditions for nature's crew of decomposers—the bacteria, fungi, and bigger creatures such as sow bugs and worms—to go to work. Browns, Greens, Air and Water are the "big four" that will keep every compost pile happy.
Composting is as easy as 1,2,3:
Chop materials so they break down more quickly.
Mix "browns" (dry woody, materials) with "greens" (moist, green materials). Learn more about what you can compost.
Maintain air & water balance by keeping compost as moist as a wrung-out sponge.
This video presents the basics about what to put in your bin, and how to build and maintain a compost pile.