Your wattage is the same, whether you are powering the device at 120V AC or through an inverter powering it from 12V. Since wattage is amps X volts, the amperage is going to be about 10X at 12V than it will be at 120. (Actually a bit more since there will be inverter efficiency losses).
What you need to do is determine what you want to run & for how long so you can determine the number of amp/hours you plan to consume. For example, if you have a 240 watt device that you plan to run for 3 hours, you will use 240/12 or 20 amps at 12V. Over 3 hours that is 60 amp/hrs that you will need to put back in your batteries to make up for what you used. Again, you will actually need to put back more since there is efficiency losses, both with the inverter & charging the batteries.
You also need to determine the amp hour capacities of your batteries. True deep cycle batteries will have published amp/hr ratings. You do not want to draw down your batteries more than 50%, so if you are going to depend on batteries alone, you will need 2X the battery capacity of your calculated usage.
You also need to think about how you plan to put the energy back into your batteries. A generator through your converter, solar, recharging by your tow vehicle are all possibilities.
A useful couple of web pages dealing with batteries are Mark Nemeth's
12V Side of Life, part 1 & 2.