How big is your yard or the intended space that you think you will be composting at? That could help determine which composting methods or bins or free-style piles that you can do.

Start at the beginning and learn about composting. The link below is to about the best composting tutorial
I have seen.

Here is a link that might be useful: Composting Tutorial

My yard is large, but the vegetable garden is small right now (about 10' by 4') and a few sunny spots here and there where I put some herbs. We have dogs, so a pile won't work.

Thanks for the link, I will read that to learn about it.

It sounds like you'll need a bin of some sort. You can use something as simple as a circle of wire fencing, or get an inexpensive plastic sheet type that forms into a circle, or a more expensive enclosed rigid plastic bin with a lid.