I'll assume you need help in chosing the proper inverter. 

You'll need the wattage of the fridge.  Look on the fridge's data plate.  I would then double the wattage to purchase the inverter of that rating.  A fridge has a motor to compress the refridgerant gas.  Motors are known to draw about double the running current while starting.  You don't want the inverter's overloads to shutdown the inverter.  You'll lose your food to spoilage and your health to food poisoning if that happens.

Then you'll need to purchase a battery that will hold enough power for as long as you're running it.  I would also recommend getting two 6 volt golf cart batteries instead of two 12 volt batteries.  Having batteries in series avoids a bunch of problems.