RV toilets simply drain by gravity into a holding tank (the black tank). The toilets seal with a ball valve at the bottom to seal out gasses and the holding tanks are vented through the roof.
We have an RV toilet with ceramic bowl and foot flush. Lift the lever with your toe and the bowl fills, giving you a nice high water level like at home. Water keeps the solids from sticking as they are deposited in the bowl. Step on the lever and the ball valve opens allowing the waste to flow into the black tank.
We have not had the need for a sprayer to keep the bowl clean thus far. The reason RV toilets have this ball valve and not an internal trap like a home toilet is to allow you to flush with less water, thereby minimizing water usage and maximizing tank capacity when dry camping (no hookups).
A small amount of water remains on the ball valve as an airtight odor seal.
Your black tank doesn't have to be directly under your toilet but shouldn't be far away or uphill either. You can use 3" PVC to make the connections but I wouldn't have more than one 90* elbow.