Upgrading computers is easy, since they're designed to be modular. Much harder than the physical act of upgrading a computer is choosing the correct component to buy.

When you say you want to learn "how they work," do you mean you want to know how a computer's hardware works, or how a computer's software works, or how the software interfaces with the hardware? These are really different things. I built my own computer and am pretty proficient with software, but if you asked me how the computer actually runs I'd stare at you and say "electrons."

When you're interested in learning something technical and you don't have a lot of money, keep in mind that several universities are now offering lectures for free online.

If you're interested in an introduction to electrical engineering, you should check out MIT's course. It's available on Youtube: https://www.youtube.com/watch?v=3S4cNfl0YF0 .

If you're interested more in the software side of things, try this one: https://www.youtube.com/watch?v=k6U-i4gXkLM .

EDIT: I should add--this is the secret of all of the people whom you ask for help when your computer is acting up. We ask you questions about what's wrong until we get a good idea of the problem, and then we go to Google and type in the problem.