Your hydrometer is your friend. In the beginning it tells you how strong your cider might be. Along the way, it tells you how your ferment is doing. At the end you can use it to determine how much priming sugar to add and how much alcohol your cider has in it. Accurate readings and understanding what they mean are essential.
First, don't expect accuracy from cheap hydrometers. Second, it helps to have a hydrometer that covers specific gravity from about 1.070 to less than 1.000. It also helps to have a finish hydrometer that covers a range from about 1.020 to 0.090.
Hydrometers are referenced to pure water at a specific temp, commonly 60 deg Fahrenheit. That means that any dissolved compounds like sugar make pure water denser (higher SG) and any liquids other than water in the mix make it less dense (alcohol) or denser than pure water. The reference temp for every hydrometer I have ever seen is written in fine print on the hydrometer somewhere. If you think about it, cold water is denser than warm water. Salty water is denser than fresh water. A mixture of alcohol and water is less dense than pure water.
Sound complicated? Yep, it is. Don't let that zap your mind. Learn how this simple measurement device works and you will be making accurate measurements. Miss some of those finer points and your hydrometer will make a fool of you.
So in the beginning there is apple juice, a mixture of vegetable solids, dissolved sugar, and water. Your hydrometer is built to reference everything to pure water which means no other liquids mixed in, nothing dissolved in it, and no small particles dispersed in it (e.g. distilled water). Right from the beginning, you probably have some vegetable solids which makes your first reading imprecise if you are trying to gauge how much sugar is in solution. In general, we all ignore this error because there is little you can do to correct it and even if you could it doesn't make much difference.
At the end, it gets a little more complicated. When fermentation stops or slows, you probably have a cider cleared of most vegetable solids but you certainly have a mix of alcohol, water, carbon dioxide, and perhaps a little residual sugar. I see lots of references in these fora to final gravities of less than 1.000. If all the sugar is metabolized to alcohol, you now have a mixture of water and alcohol which is sure to have a SG less than 1.000 since the SG of ethyl alcohol is 0.787. So a mixture of pure water with 5% ethanol should be around 0.989. This would be the case where all the sugar has been converted to alcohol. To make it a little more complicated, if the solution is saturated with CO2, the SG is changed as well.
Don't throw up your hands in despair. All is not lost. First, buy a good general purpose hydrometer. I buy mine from Cole Palmer and they run about $35. I always have two on had since any hydrometer is one careless movement away from a pile of broken glass just when I need it most. I also own a finish hydrometer recommended by my friend Bembel (see his posts) that I bought on Amazon.
De-gas you fermented sample and bring it down to the calibration temp of the hydrometer you are using. I typically heat my sample in a Pyrex measuring cup floating in 180 deg water then agitate it with a power whisk (Amazon again). This removes the CO2 and most of the alcohol. At that point, I know I am working with a mixture of water and sugar (if there is any left), not a mixture of water, alcohol, and sugar.
Finally, I wonder about the manufacturer of your hydrometer. Always measure at the bottom of the meniscus since the top and bottom are related to the diameter of the hydrometer. I suspect yours is made in China and they screwed up the instructions in translation. Mark's advice should be heeded. Test you hydrometer in distilled water and if it deviates from 1.000 at the reference temp, use this as a correction factor.
You can geek it out a little more by mixing up reference solutions of water and salt. See C. Jolicour's excellent manual on making cider.
Some people on this forum just wing it and probably make some fine cider. I like to get into the details but I doubt that my cider gives me a better buzz than theirs.
