Categories and Subcategories Question

Hello, I am a student currently desiging our schools website and I have decided to go with WordPress for our school site. I have redesigned the Gila theme for our site and have now moved onto the process of pasting information from our old site onto our new one and I have come into a few problems.

Our old site is divided up into different sections, just as most sites are (aka, Departments, Classes, etc.) and inside each category is a subcategory that people can go into to read more about said subcategory (like placing “Art Department” in the Departments category). I plan on doing the same thing with the new site, but I can’t seem to actually place my new category inside of a previous category and get it to show up in a list of other categories.

Put more simply, when I place a new post inside of a subcategory, I no longer see the parent category on the category list on the homepage, and when I place it inside both the parent category and the new subcategory, I still end up seeing the new post inside of the parent category but not a link to go to the new subcategory.

I hope I am not being too confusing to you all but this is the only way that I can think of saying this.