The easiest way to test a microphone is with the Sound Recorder accessory in Windows. Press the rightmost button to start recording, speak into the microphone, and watch the green line on the screen. If the line doesn't move, the computer isn't hearing anything.
Make sure the microphone is plugged into the MIC jack on your sound card. Also check the sound mixer program (see your sound card's documentation for instructions) to make sure that the microphone input level is turned up and the recording source is set to the microphone.
If this is a new microphone that you're trying out for the first time, also make sure you have the correct type of microphone. Most microphones are the condenser type, but there are also carbon microphones, and your sound card may have a preference or setting that determines which one to use. Also check the microphone's specifications against the sound card's requirements. The spec. that trips most people up is the impedance or Ohm rating; for example, a 2K Ohm microphone in a sound card rated at 600 Ohms simply will not work.