A hydrometer does one thing: it floats higher in a denser liquid. Unfermented wort is full of dissolved sugar, so it is denser than water and the stem rides high; as the yeast turns that sugar into alcohol and carbon dioxide the liquid gets lighter and the stem sinks. That is the whole instrument. Everything else (the scales printed up the stem, the calibration temperature etched near the bottom, the trial jar it lives in) exists to make the number you read off it comparable to the number you read last time, which is the only reason to take a reading at all.
Reading it without fooling yourself
Fill the trial jar, not the fermenter, and give the hydrometer a spin as you let it go so the bubbles clinging to the stem come off; a bubble skin is worth several degrees and always in the flattering direction. Let it settle, then get your eye level with the surface and read the bottom of the meniscus, the low point of the curve where the liquid climbs the glass. Reading the top of the curve instead is the single most common way a home reading comes out two or three degrees high, and it does it consistently, which is worse than doing it randomly.
Degrees, not decimals
Brewers talk in specific gravity, 1.048, 1.011: but every calculation you will do treats those as degrees above water: 48 and 11. HMRC's guide works in exactly those degrees, and so does this site, because the arithmetic reads better and the difference between two readings is the thing that matters. A beer that went in at 48 and finished at 11 attenuated 37 degrees, and that single number is what the strength, the attenuation and the answer to 'has it finished?' are all built from.
Temperature is not a detail
Every hydrometer is calibrated to a temperature, usually 20°C, and the liquid it is floating in expands as it warms. Read a 30°C sample against a 20°C hydrometer and you will be several degrees light. HMRC's guide fixes alcoholic strength at 20°C for exactly this reason, and the correction card that came with your instrument exists to bring a warmer or colder reading back to it. Cool the sample or apply the card, but do not skip it and then compare that reading with one taken at a different temperature.
Two readings, not one
A single reading tells you very little. Take one before the yeast goes in, as soon as the fermenter is full (HMRC's guide is specific that the original gravity is established before fermentation starts, normally within an hour) and take the other only once two readings two or three days apart agree. That second condition is not fussiness: a gravity that has stalled looks exactly like a gravity that has finished, and priming a stalled beer is how bottles come apart.
Questions people ask about hydrometer
Does a beer hydrometer differ from a wine hydrometer?
Not in what it measures. Both read the density of the liquid; the difference is which scales are printed on the stem and, sometimes, the range. A hydrometer that reaches 1.170 for a heavy must will be coarser at the beer end of the scale, so a dedicated brewing hydrometer is easier to read on a 1.048 wort.
What is an alcohol hydrometer, and will it read my beer?
An alcoholmeter is calibrated for a mixture of alcohol and water only, which is what a distiller has after distillation. Beer is alcohol, water and everything the yeast did not eat, so an alcoholmeter floated in beer reads nonsense. Use a brewing hydrometer and two readings.
Mine broke. Can I use a refractometer instead?
For the first reading, yes, and it is more convenient because it needs two drops. For the reading after fermentation, no, not directly: alcohol bends light differently from sugar, so a refractometer in finished beer needs a correction that itself needs the original reading. Most brewers use both, one at each end.
How accurate is a home hydrometer?
Around a degree, if it is clean, spun free of bubbles, read at the meniscus and at its calibration temperature. That is comfortably good enough for the arithmetic on this site. It is not good enough for a label or for duty: HMRC's guide sets out a laboratory method for those, and it involves distillation.