Use a multimeter. In my smaller trailer, there are two 12V circuits for the lights. Are all of your lights out? If so, I'd suspect a faulty negative wire back to the battery (some call this a "ground", but that's not quite accurate - the 12V DC current makes a complete trip from the battery, through the lights, and back to the battery.) You can check for voltage by connecting your multimeter's positive probe to a positive plug contact at a light and then, using a long jumper wire attached to your multimeter's negative probe running all the way back to the negative post of the battery. This bypasses all the trailer's negative wiring. If you get voltage, the problem is in the negative wiring. You can reverse the jumper wire to see if a positive circuit is faulty.
You can also test for continuity by first disconnecting the battery, and then using a jumper wire to reach the end of the wire you are probing at a socket.
I had a mouse chew through a positive feed wire to one of my tail lights and I simply ran a replacement wire past the chewed portion, splicing it where I had access.
- Jack