What tools for measuring specific gravity are available to the homebrewer? EG: refractometer, hydrometer.
What scale do they measure? EG: Brix, plato
Typically a Hydrometer measures (or at least mine measures) Specific gravity, potential alcohol, and/or Balling. Refractometers measure Brix.
Most beer recipes use SG as their measurement. For example, according to NorthernBrewer, their California Common kit has an OG of 1.047. Hypothetically if you were to measure an amount of pure water (just H-O-H) at the calibration temperature (typically somewhere around 60F-70F), you would get 1.000. Warmer liquids are not as dense, therefore the same volume of pure water at 150F would be much lower. Similarly, that same sample of pure water at 35F would be much more dense.
Refractometers? I'm sorry I never owned one, so I can't speak about them other than they are significantly expensive and that since your sample is 3-4 drops of liquid, and not 3-4 liquid ounces... temperature is not much of an issue, and the degrees of Brix measures the amount of sugar, and there IS a conversion from Brix to SG, but I don't know it.
Since there hasn't been much activity on the question, this is what I'm looking for. Any more comprehensive answers?