The truth of the matter is there are about as many opinions on what to do, how to treat the holding tanks, as there are license plates pulling said campers.
Some just use water.
Most all will tell you not to leave the black tank open because you want plenty of water in this tank to break down solids and prevent build up or drying out of solids, some times referred to as the "poop pyramid".
Most will tell you to leave the gray tank closed also to allow you to have "cleaner" water to rinse the tank hose after dumping the black tank. Some say leave it open and then close before a day or two before you leave to build up enough to rinse the hose after the last black tank dump and prior to storage.
Some use RV toilet chemicals.
Some use the "Geo" method mentioned above.
Here is the "CincyGus" method. You'll notice similarities to most of the above ;-)
I put a couple of gallons of water in each tank prior to leaving for the trip by holding down the flush valve on the toilet and running a little water in each of the sinks. This makes sure I don't have a dried out "P" trap that will allow tank smells come back into the camper during my journey as I often leave a roof vent open to cool the camper when it's hot. I add a cap full of liquid Calcon water softner and a handful of the cheapest power laundry detergent I can buy at the dollar store to the black tank.
This foams up a bit and swishes around the tank on my trip to the campground. Coats the sides and is supposed to prevent anything from sticking to the sides of the tanks.
When camping with full hook ups, I leave both tanks closed. I monitor the tanks and generally the gray will fill first. When it does, I decide how much I should drain Maybe all, maybe half) based on how full the black tank is. If it's less than half full, I'll drain it completely and close it again. My goal is to have at least a 1/2 to 3/4 a tank of gray water to flush the hose when I do finally have to drain the black. The main reason being, a hose that has had a black tank drained that is not rinsed with gray/fresh water can stink, especially if some particles are left in the hose. If you have very tight, secure fittings, you might not have an issue.
Same method when camping without hookups and using our tote or a dump station. I want to be able to run a good 10-20 gallons through the hose any time I have finished dumping the black tank.
Once done, I put a couple of gallons back in the tanks, put my water softner and detergent in prior to the ride home and I'm getting the benefit of a good sloshing cleaning of my sensors and tanks during the ride home. That stuff stays in the tanks until the next time we go camping.
Works for me, have no smells, always have a clean dump hose, never had a clog or "Pyramid" and might spend $10 a year for the above. If I'm throwing it down the toilet, I'm ok with that. I've spent more on a crappy meal before.