You can work on it while mounted on the floor. But it's so much easier to pull it and carry it outside.
You will need a new foam seal for the toilet and maybe a piece of cardboard.
Turn off the water supply and the water pump. Open a sink drain to bleed the pressure out of the water lines.
Place the cardboard on the floor in front of the toilet. Remove the two nuts holding the toilet to the floor. If I remember correctly they are 7/16" nuts. Tilt the toilet forward and unscrew the water hose from the back of the toilet valve. Lift the toilet up off the floor and be amazed at how light and extremely cheap feeling the toilet is. You can set the toilet on the cardboard to catch any drips, then carry the toilet and cardboard out of the trailer.
If you want to add a hand sprayer, now is the time to do it. You will see a sealed barbed fitting coming off the back of the flush valve. Go to Lowes,/Home Depot and buy a standard kitchen sink sprayer and hose combination (apprx $10) Cut the fitting off the end of the new sprayer hose. Cut the tip off the barbed fitting on the water valve. Slide the sprayer hose up onto the barbed fitting and secure with a hose clamp.
Put a new foam gasket on the black tank. Set the toilet on the existing bolts and attach the water lines.Sit on the toilet to compress the new gasket. Tighten the two nuts that hold the toilet down to the floor. If needed have your friend sit on the toiled while you tighten the bolts.
Done.