I don't know of any online courses -- but the manual of one of the professional courses (Barnett's) is online. You can try searching the previous threads.

Personally, I would suggest buying a good bicycle repair manual, such as Bicycling Magazine's Complete guide to Bicycle Repair or Zinn and the Art of (Road/Mountain) Bike Maintenance. They're each about $20 new.
I have both of these and they've been very helpful. I've gone from not knowing how to lube a chain to wrapping bar tape and overhauling hubs and headsets.
I was nervous at first to work on the bike (what if I couldn't put it together again?), but I figured if I messed up, my LBS would gladly bail me out.