How do I output a list of custom post type categories?

Let’s say I have a custom post type of products and within that I have categories such as coats, shoes, shirts, etc. Is there an easy way to output the names these of these categories with a link to a page that will display the contents of that category (eg. /products/hats)?

Ideally I’d like to output my custom post type categories (taxonomies?) into columns on my home page, complete with an image associated for each post type category. Problem is, I can’t seem to do much except blindly list all my custom post types. There seems to be very little documentation on calling a list of categories.

Has anyone done this before or know of a template that currently performs this functionality? I’m stumped.