To have a category page list out products for that category you will want to add a dynamic list to your category template.
Connect that list to your products collection. It should then list out all of you products. Then in the settings for that list you should be able to filter the list based on current category. The filter option literally says filter by current category. This should limit the list to only products you have tagged with that category.
Hope that helps. If not feel free to post your read only link so we can have a closer look.