I'm trying to get a feeling on how hard it is to build your own computer,
It's not hard at all, once you get the hang of it. If you've never built one, I'd suggest locating a "mom and pop" type computer store that will build a machine to your requests and answer any questions you might have. As that computer gets older, you'll eventually want to add in a new drive or more ram (but remember, if you bought a system from someone, make sure you're not going to void any warranty by opening it up yourself).
Or, buy an old machine and take that thing apart. The power supply goes to the main board and the drives. Cables go from the board to the drives to transmit data. Your cd drive will (usually)have an extra cable to transmit redbook audio from the drive to your sound card. Ram has a couple of brackets to hold it in. Most boards have an agp slot for the video card, and your modem, etc will probably be pci.
The hardest part (in my opinion) is getting a motherboard, ram, and processor to all be compatible with each other. I generally try to buy all three of those from the same vendor, since if you get part A from one vendor and part B from another, and they don't work together, both vendors will probably tell you it's the other vendor's problem. Buying all three together eliminates the "pass the buck" from support.