Most likely it runs of gas and 120V AC. There are some model fridges that have 3 way capability and can also run off the 12V battery. If you can find out what make/model it is you can download the manuals from Dometics website.
Most likely it is a 2 way fridge, propane and powe(120v) Just put the switch on auto and it will automatically go to propane if you unplug the trailer from shore power, but be sure the propane bottle valves are open.