Measuring it, and the temperature trap
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The two instruments
A hydrometer floats in a cup of syrup and you read it where the surface crosses the scale. A refractometer measures how the syrup bends light and converts that to Brix. The hydrometer is cheap, robust and needs a decent volume of syrup; the refractometer needs a drop and costs more.
Where the temperature trap sits
Syrup is denser cold than hot, so the same syrup reads differently at different temperatures. Syrup hydrometers carry two marks for this reason, a hot test and a cold test, and the hot mark is an allowance for reading syrup straight off the heat. Using the cold mark on hot syrup, or the reverse, is the single most common way a producer finishes to the wrong density while doing everything else right.
Calibration is part of the number
The regulations say this out loud. Vermont specifies its density at 60 °F on instruments calibrated at 60 °F, which is an admission that the figure means nothing without both. A refractometer with automatic temperature compensation handles part of this and does not excuse you from knowing what it is compensating to.
Read it clean
Sediment, bubbles and film on the surface all move a hydrometer reading. Fill the cup properly, let it settle, read at eye level and read the same way every time. A reading taken in a hurry on a cloudy sample is a number about that moment rather than about the batch.
Record it against the batch
The reading, the temperature, which instrument and which mark, and the batch code. A number in a log with those four beside it is evidence; a number remembered is a recollection, and the two look identical until somebody asks.