While a beer hydrometer can be used to monitor the progression of fermentation, a lot of home brewers have difficulty getting an accurate reading. Below is an easy to follow guide on how to use your hydrometer.
Hydrometer readings are typically taken before pitching the yeast and after visible signs of fermentation have ceased. It is generally not recommended to take more samples than necessary because each time the fermenter is opened to draw out wort, you are introducing the risk for contamination.
Place the wort sample in a vessel big enough to allow the hydrometer to freely float without hitting the bottom or sides of the container. Use a test tube, or you can sometimes use the container the hydrometer came in. Once the liquid is in the container, place the hydrometer in the sample and give it a gentle spin. The hydrometer will eventually settle and you can take your reading. Sometimes the hydrometer will stick to the side of your vessel, so make sure it is floating freely before you take the reading!
General rule of thumb is that if you take two hydrometer readings 24-48hrs apart, and you get the same reading both times, fermentation is complete and you can now bottle/keg your beer.
Important Note: After you are finished, do not return your sample to the fermenter, as it could cause contamination. Instead, taste the sample to get an idea of what to expect from the final product, and discard it.