Upon buying such a vehicle their are a few steps that you can take to make sure their are no obvious underlying problems.
Firstly inspect the trailer thoroughly, don't be afraid to check to roof for damage or signs of water penetration. It is also best to check that all the electrical systems are in working order. I would advise having the previous owner guide you through the features of the trailer and ask them to carry out demonstrations on how to use to equipment, this will give you peace of mind that everything is in order. It would also be a wise idea to inspect the underside of the trailer for rust or any mechanical hitches such as the rigidity of the chassis.
Once you have checked out the trailer and feel happy with its current state it would be useful to have a second opinion, invite a friend/ relative to come and view the trailer, they may pick up on things which you may not have spotted. After this it would be a great idea to get a professional mechanic to check over the trailer. They will be able to double check that nothing affecting the transport ability or stability of the trailer like wheels, bearings and so fourth are in good order.
Finally once all these checks have been done and you are satisfied that the trailer is for you, get a background check on the trailer, this will highlight if the trailer has been involved in any traffic collisions or if the trailer is stolen.
Good luck !!