Hydrometers are tools that can be used to determine the amount of fermentation that has taken place in your beer or wine. The hydrometer does not measure the alcohol level of a brew, but can be used to determine this by taking a reading before and after fermentation. The density of a liquid is what is measured by the hydrometer. Hydrometers are accurate tools, but the accuracy of YOUR estimate of what the alcohol level of your brew is will only be as accurate as YOUR calculations.
The use of the hydrometer is one way to determine the alcohol level of your brew, but not the only one. There are other scientific apparatus' that can do the same thing, but they are far more costly than a hydrometer. One way to determine the alcohol level of your brew is knowing how to use a hydrometer, but it is not the tastiest! Sampling and experience are the other way to determine this. Knowledge of both techniques will enhance the other, no doubt.
Always test your hydrometer when you first get it. To do this, place the hydrometer in a testing jar filled with enough water to make the instrument float. Spin the hydrometer to dislodge any bubbles that may be in the water, which would otherwise cause you to get a false reading - too high. This same testing jar can be used to measure the specific gravity of your wort and your beer after fermentation but before carbonation. The hydrometer should measure the weight of water on the specific gravity scale as 1.000 at 68° F. You always want to measure the specific gravity at 68° F, to ensure an accurate reading. Read the number on the paper where the liquid crosses the stem of the hydrometer
There are three scales on the hydrometer, but the home brewer is concerned with only two of these - the Potential Alcohol and the Specific Gravity - and knowing what these scales are for is essential to know how to use a hydrometer. The potential alcohol scale is used to read an estimate of how much alcohol can possibly be made in your brew. The specific gravity scale is used to read a comparison of the density of your brew with the density of water. So the first measurement you take is done by placing the hydrometer in the test jar with enough of your wort (at room temperature) to make the hydrometer float. Note these measurements in your home brew recipe journal.
After you think your fermentation is complete, repeat the process and take a second reading of how much potential alcohol is left. By simply subtracting the initial amount with the leftover amount, you can determine how much alcohol is in your brew! The second specific gravity reading will let you know how much unfermented sugars combined with other unfermentables that are left in your brew. This will tell you how much of your ingredients ended up as unfermentables (starches and dextrins), or that your beer needs longer to ferment.
At this point, and at all points throughout the brewing process, I feel it is imperative to taste your wort. By knowing how the sweetness, malt flavors, and body develops throughout the brewing process, especially in relation to knowing the specific gravity and potential alcohol of your brew, you will develop your sensory knowledge of brewcraft. This, in combination with knowing how to use a hydrometer, will enhance your ability to taste and smell vagarious qualities of the beer you produce.
Another benefit of knowing how to use a hydrometer is that a hydrometer can be used to check whether your fermentation has completed. To do this, you will take a reading two days apart and compare results. If there is any change in the results, then your brew was still actively fermenting during this time. If the reading remains the same, then fermentation is completed, and you can move on to kegging or bottling your brew.
Knowing how to use a hydrometer is a useful skill in the world of home brewing, and can lend confidence to your knowledge of brewing.