Are you looking to start a service that requires nothing more than the trailer? Or something that may require you to spend a little? Maybe a grocery shopping trailer for all the old farts? You'd need to find a way to refrigerate it. Just get their shopping list, or have them order it online and you pick it up and they pay you. If you could get 10-12 people to do it at the same time, you could charge 10-20 per person.
You're going to ruin a perfectly good trailer if you're moving trash. Maybe it's just me, but I like having nice things and try not to ruin them.
Just post a series of ads: "I have a 15ft trailer, what do you need?", "Moving? Let me help!", "I can help you move your furniture", blahblahblah
Think about it like SEO (search engine optimization). The more variations of what you're capable of the better because people can't read between lines.