Here's the steps to calculate:
Say optimim moisture content is 12% and soils are at 8%, and maximum dry unit weight is 110 lbs/cufic foot. You need to increase moisture by (12%-8%)x110 or 4.4 lbs/cubic foot. Since there are about 8.34 lbs/gallon, you need 4.4/8.34=0.53 gallons/cf. This is per cubic foot at 100% compaction; you would need to factor lower by in place density divided by max dry density.