The system is quite simple -- You merely run a good wire from the Tow Vehicle battery's positive post (with a 20-30A auto-disconnect circuit breaker) to the 7-pin Bargman/Pollack trailer connector's battery
Wire sizes folks have used range from #10 to #6 -- I figure as long as I am running it, the bigger the better (The less voltage loss, the truer the picture the TV charge system gets of the trailer battery
-- Opinions vary on this).
If you don't have a 7-pin connector, you should install one because it will accommodate the charge lead and the brakes
lead, plus an auxiliary lead for whatever.
I also ran a negative/return wire of the same size between the connector (common ground) and the battery's negative post to ensure that I had a good path, plus I made a good connection between that wire and the TV frame. Overkill, perhaps, but the return wiring has to handle ALL the returns for the various wires to the trailer.
Pin-outs for the connector wiring can be found here:
trailer wiring diagram can be found here:
Many folks also install a cut-off relay on the charging wire, controlled by the TV ignition switch, to prevent discharging the TV battery by a trailer load (fridge) while sitting with engine off.
Separate charging systems would be the best possible way, but they would also be $$ -- Dual alternator system are available in the Marine world.