Consider the trailer it's own vehicle and lock it away as such. A trailer should carry it's own locks, just like your bike does.
Pulling a long chain lock through both wheels is quite effective (although a bit cumbersome if you have a wide trailer). So is locking both wheels to fixed objects like lanterns. Depending on your threat assessment, you could even go for the overkill and lock everything that has enough room to fit a lock through to something.
Key in all this is to consider the bike trailer it's own vehicle. Lock your bike like you'd usually lock it, remove the trailer and park it somewhere safe. Locks will help you with that, just like they do with your bike.