Originally Posted by gsa103

REI and Performance Bike both offer introductory classes. Many local bike shops will also have an occasional class. Beyond that the web is a great source of information, you can find videos on how to do just about anything.

Beyond that, bike breakdowns basically fall into three categories:
1) Flat tires
2) Crashes
3) Component failure

The over-whelming majority of issues are from flat tires. Carry a spare tube, pump or CO2, patch kit and know how to change a tire. Practice changing the front (& especially rear) tire in the comfort of your garage. Once you've done it a half dozen times, you should be able to repair a tire and be back on the road in ~15 min or less.

I'm not going to say much on crashes. There's a wealth of information on mountain bike repairs that are equally applicable. Make sure your multi-tool has a chain tool and carry a spare quick-link. That will let you repair chains. Limit screws on the derailuers can be used to set a gear if you've broken a shifter.

Beyond flat tires (which are fixable), a well-maintained bicycle should essentially never have a sudden failure that would leave you stranded. The key is listening and inspecting your bike on a regular basis. Make sure the wheels are true, the brakes work, and the drivetrain runs smoothly. If you address issues when they're minor, you're not at risk for a significant failure. The vast majority of things should be fixed in the comfort of your garage, not on the road. And lastly, if you've just fixed/modified something carry the required adjustment tool with you and don't set out on a 100mi ride to nowhere on something that's untested. When I installed a new chain, the first thing I did was mash up the steepest grade in my neighborhood, just to make sure I could trust it on a longer ride.