Laptop fans are an important aspect of cooling off the internal workings of your computer. They suck heat off the motherboard and processor, and blow hot air away from them--much like a radiator fan blows hot air away from a car engine. Overheating of your computer can cause malfunctions and damage to important components within, which can mean costly repairs. Testing your laptop's fan is important and easy enough that you should do it with some regularity.
Turn your computer on. Depending on the type of laptop, you should be able to tell where a cooling fan is located and where it blows the hot air out. Place your ear up to that point in the body of your laptop and listen for a fan. If it is running, you should be able to hear it. If you can't hear it, you can try further methods to test your fan.
Place a piece of paper in front of the fan output. You may not be able to hear the fan, but you will be able to see if a piece of paper is being blown about, even if it's just a little bit. This will also determine if the fan is working or not.
Download and run a program such as BurninTest, SpeedTest or Core Temp. These programs, all free online, push your computer processor to its limits and test the speed and heat coming off the processor. It tests the stress that your computer can handle, as well as diagnosing errors caused by heat. Through these results, you may find out how efficiently your laptop fan is performing, and therefore, if it is working properly.
If you determine the fan is not working properly, turn your computer off and blow one or two streams of compressed air into your fan. This will hopefully dislodge any dust or debris from your computer and its cooling unit. Dust and debris can impede your fan's natural motion, and therefore cause it to work harder in order to do its job. Clean your fan and turn your computer on once again, testing to hear if it sounds better or testing that it doesn't produce as much heat as it did before.