First, work out how much power your device uses in amps. Multiply the total amps by the number of hours the device will be used before the battery will be recharged. Add 15% to this figure for safety. Then, because deep cycle batteries should not be discharged below 50% of their rated capacity, multiple by two.
E.g. A 12 volt fridge draws an average of four amps, and you want it to run for 12 hours without recharging the battery.
4 Amps x 12 = 48 Amp hours
Add 15% = 55 Amp hours
Multiply by 2 = 110 Amp hours