I never knew about them due to my preference to not join any formal affiliations. How do they work? Do I choose a specific place to build one? Do I get my own little citizens? Can I build one in a town? What? What? WHAT?

Each of the three Great Houses has one.
It's on a predetermined location (usually far from any city,) but each stronghold is very different depending on which Great House you're in.
They are rather large, and usually come with a protective wall around them too.

Info on the Wiki: http://www.uesp.net/wiki/Morrowind:Stronghold

As you progress through the Great House quests, you will eventually get the option to buy a Land Deed and build you're own home. It then takes a few weeks (in game time) and there are some minor quests to accomplish for it to be finished.
You can hire guards and miners and a few people to live there as help.

There are some mods that make them more detailed. Like "Uvirith's Legacy" and the "Redoran LGNPC"

edit: Also, with the Bloodmoon expansion, you can do the East Empire Company Questline to build the entire little town of Raven Rock, which also gives you a large house to own.