What would be a good way to start learning?

ashtoast, one of the first things to get into would be to read schematics and how to approach proper trouble shooting. Collect as much information as you can about the devices you are interested in. get as many guides and service manuals as possible, you'll be surprised how handy they will become. Try to find most common errors and their fixes. Seriously, that is have the battle. Just check on here (ifixit) the amount of gray screen issues, overheating issues of Xbox's and PS3's. That way you will not just have to go and keep replacing parts. Of course a knowledge in basic electronics will help as well, it's nice to know the difference between a capacitor and resistor. Another really important thing, in my opinion of course, is to learn how to properly use a multimeter. Soldering will become another issue. Most devices are easier fixed with a hot air station due to the fact that they are using a lot of SMD components. You may also consider investing in a small reflow, or rework, station. Not very expensive but a great tool to have. Of you need broken stuff, you can always try ebay. I've gotten tons of broken iPods, cameras and other small electronics for decent prices. The other places are pawnshops, garage sales, and Craigslist etc. There are of course many many more things, but I do hope that this will help.