The only way to truly test a breaker is to draw a known load through it and see if it trips at the proper amperage rating. This is not practical for a DIY'er (heck, even if you have an electrician on site, you would be cheaper just replacing it vs. this kind of testing).
A couple of things that you can do yourself that will give you a pretty good idea about the breaker though....Test the voltage output of the breaker.
If no voltage, check to see if it is tripped. If it is tripped, disconnect the load (circuit) wiring and reset it, then test again. If breaker trips again or has no voltage output (with no load), breaker is bad.
If no voltage and it is not tripped, try resetting it anyway. If still no voltage, breaker is bad.
If breaker appears to have proper voltage output, reconnect load and test again. If breaker trips, you have a circuit problem. If breaker has proper voltage and your circuit still does not work, you have a circuit problem.
If you have a circuit problem, here are 2 possibilities:
First, Not 100% guaranteed, but works almost all of the time. If it doesn't, you will be stuck opening each receptacle on the circuit until you find the problem.
Turn on all of your non-working lights and plug lamps into any non-working receptacles. Make sure that any computers, or other sensitive electronics are not plugged into this circuit. Take a lamp or an extension cord around to the all of the receptacles on this circuit. DON'T rule out the working receptacles either. Try them too. Plug it in and wiggle the plug (hard enough to wiggle the receptacle too). You will probably find one where doing this suddenly causes your non-working lights/receptacles to come back to life. This will be your culprit.
A lot of homes are wired with receptacles using 'stab-in-the-back' connections. These are actually still in use and are deemed safe for installation. The problem is that they have a terrible failure rate. The term 'stab-in-the-back' also applies to what they do to you later. Any replacement should have screw terminal connections.
Second, if you are in a double-wide, is to check the crossover connections. This is where the power is crossed over to the half of the home that does not have the breaker panel. This is almost always located somewhere under the home along the 'marriage line'. There are many different variations for this. Email me if this appears to be an issue and you need more info.