Normally it's the gray water that accumulates quickly and may have to be dumped daily. This can be handled by a 20 or 30 gallon tank on wheels that can be pulled to the dump station, usually by a car. It's a lot of weight to do it by hand, but can be done especially if the tank has four wheels.
The black water tank usually lasts a number of days before needing to be emptied. It is normally emptied by driving the rig to the dump station or, if available, having a mobile service do it.
For maximum convenience, choose a site with full hookups.
Have fun with your new hobby. It is the best family memory-maker on wheels.