The legal part of the transfer is usually the same as purchasing a car. SOME states didn't title travel trailers in the distant past, and lots of people seem to take a very sloppy approach to titles when they're selling ("Bill of sale only" offers are common even in title states, because they've no idea where the title is.)
What other paperwork is involved depends on what state the trailer is titled in, and what state you live in. I'd recommend checking with the agency that manages vehicle titles and registration in your home state, they'll hopefully provide you with the forms you'll need and what requirements must be met. It might be as easy as finding the agency's website.
To give you the example for Texas, if you have a valid title from another state that's duly signed over to you, you have to surrender that plus sales taxes and registration & title fees to the State of Texas and they'll issue you Texas title as long as nothing fishy turns up in the process. It's easier if you have a bill of sale to go along with the title, though if they do it like they do cars for newer ones, they'll charge you the higher of the bill-of-sale value or the blue book value. When I bought the Argosy in 2011 they accepted the bill-of-sale value, but then a book value on a '75 would probably have been lower anyway!
The biggest thing to me would be not to buy anything sight-unseen. A used trailer might be in excellent as-described condition, there may be problems the seller genuinely doesn't know about, or they may be selling you a pig in a poke. There's no substitute for a trustworthy inspection of the trailer.
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill