Trouble shooting a garage door opener is just a matter of taking it step by step until you find the issue. There are quite a few things that could cause the door to not operate, but they are mostly small and easy to fix.
The video below goes thru the trouble shooting steps, up the need for a repairman or a replacement.
Hope this helps get you door fixed. For properly maintaining you garage door, to to help prevent other issues check out http://www.homediyfixes.com/properly-maintain-your-garage-door/