A few things. You can see it in a pile with dark green leaves on top and mostly brown stuff underneath. Or you can see it in the soil beneath your plants, as dark patches that look very much like mold. But it's more than just looking at the compost.
Compost should be a rich, dark, black color. If it's not, then there are problems with the ingredients or the process. It should smell good, too. If you have a composter, you can check out the condition of the ingredients yourself. If you don't have one, you can buy composting bins.