You should really test your alarm weekly!
If your system is monitored, always have the central station place your account on "test"or no response while you are testing. How you do such varies on your service provider.
Some manufacturers offer what is called a "walk test" feature, which can be found in the end user's manual. Some may not.
If your system is monitored, unless you have a daily dialer test (dictated by your contract) you should test your system for proper communications to the central station. Arm your system and trigger a signal. You may need to let your alarm ring for some time, but when your alarm is transmitting its signal, your house's phones should have no dial tone. If you hear a "fax" tone or the line doesn't go dead, you may need to have the system serviced and checked for proper line seizure.
IF the communications part passed the test, now you can move onto the next part. If you don't have a walk test feature, you may be able to use the chime mode of the system to verify each door and window on the system for being recognized by the system, otherwise this is the time a helper would really pay off.
Motion detectors vary in their testing methods, but you'll either need to walk test and verify the unit's LED for "seeing" you, as well as the system recognizing you moving around. Keep in mind, motions aren't designed to see you waving your arms, jumping, or walking towards them, they're designed to detect movement across their coverage patterns.
Smoke, CO and heat detectors should not be tested by using a match, burning paper, or other means, as that may cause damage to the units or necessitate a cleaning or maintenance. Caution should be used when doing such. In this case, I wouldn't recommend testing unless you have the unit's installation instructions or the unit has a dedicated test switch and you are extremely familiar with the units.
Low temperature and flood units can be tested in generating a condition that they are monitoring. An ice cube or a small cup/pan of water will generally work for each respective type
Panic buttons can be tested by pressing them. How your system reacts to them is dependent on programming and if such features were enabled.
Once you are satisfied everything is working the way it should be, clear and reset the system to its everyday "normal" disarmed state. Call your central station and verify the proper transmission of a signal and return the system to service.
Keep in mind, by doing such an "audit" of your system, in conjunction to paying attention to maintenance details, your likelihood of a false or malfunction does go down without you knowing about it. By no means is this a substitute for servicing or maintaining your system.