From trying a few quick searches on Youtube, I found LOTS of videos from different people for basic maintenance items. So it's easy to learn how to do things. The trick, then is threefold: know what everything is called so you can search for it, know that something needs to be done, and know enough specifics about your bike to narrow the information!
For the first and third of these, check out
http://sheldonbrown.com/The second, recognizing a problem and identifying it, is tougher to learn. To start with, you should learn what a bike tuneup entails, then learn how a properly adjusted bike should act and feel.
Here's a basic tuneup, off the top of my head:
- wipe down bike, I like to do this first so I don't get myself as dirty (just a rag is usually sufficient unless it's really dirty)
- check that wheels are true/round/dished
- check hubs for play, resistance
- check & adjust brakes
- check bottom bracket for play
- check pedal bearings for play, resistance
- check chain to see if it needs replacing
- clean & lube chain
- check shifting
- inspect all bolts for tightness (do not overtighten, just make sure they aren't loose)
- check headset for play, resistance
You should be able to search for any of the above on Youtube or Sheldon Brown's site to learn how to do that specific item.