It is done by volume so you need to start out with an accurate way to measure volume. A graduated cylinder is obviously the optimal vessel. I attached a link for one from Amazon at the bottom of this post. The main key here is accuracy. I will do it based on 100 ml, (it is always based on 100%) but since all the measurements are by volume, you can do the same thing in ounces, liters, gallons etc, just make sure you use the same type of measurement for the whole formula.
You have a whisky that is 46% ABV or 92 proof and you want to taste it at 80 proof. Your target volume is 100ml. You would add 13.04 ml of water to 86.96 ml of your 92 proof whisky. It is ok to round a bit, so you could add 13 ml water to 87 ml Whisky. The quick and dirty formula is this.
So now you take your desired proof (80) and divide by 0.92 (because it is a 92.0 proof spirit and we always move the decimal to the left by 2 spaces)which will result in 86.95652173913043 or roughly 87 ml. Subtract that from 100 and you are left with 13ml.
or for 102 proof spirit
In this case we divided 80 by 1.02
Again, this will work for any volumetric measurement, just change ml to liters or gallons or liquid ounces. If you are going to use this, just remember that in order to replicate a tasting, you need to measure accurately to begin with. Also, you obviously cannot increase the proof of a spirit. If you begin with a known volume of a spirit and water and want to know what the proof is, just reverse the calculation my multiplying the volume by the proof (Remember always move the decimal of the proof to the left by 2 spaces).
if you need to convert it to 750ml, for example, you would take your volume #'s and multiply by 7.5 (since 7.5 x 100 = 750) or to make 50 ml you divide by 2 (100/2 + 50)
Here is a link for an inexpensive graduated cylinder in 100ml, these can be found up to 4 Liters or more...
or in glass
I figure $10 is not too expensive considering what we already spend on our Whisky passion in general.
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