Battery should charge whenever you are plugged into "shore power", but, you might be surprised at how long it takes to bring the battery up to a "full charge" when you are doing this. Charging can be more complicated than it first appears, but the short version is that about 24 hours should bring you up close to where you want to be, depending on how discharged it is. The rule of thumb is not to discharge it more than 25-50% of its capacity before you start re-charging it. Your truck should charge it while you are driving- but that takes a good while and is not all that reliable and, again, even driving all day likely won't bring to where you want it after a good nights use or a couple of nights. A good charger like a "Batterey minder" is what many of us have when we have it parked at home. It does more than trickle charge it- and maintains it and changes the charge based on how "full" the battery is getting. Good converters/chargers will do this also, but the one that came stock with your trailer probably isn't fancy enough. People also use solar panels for charging but, again, it takes more than one good panel usually to get a battery charged up----but it isn't a bad way to go if you camp where there is a lot of sun and some have successfully used it pretty exclusively.
Rick