Great advice, but I like to dump like Frank-VA adviced. I never have the black-water tank valve and grey-water valve or valves open at the same time. I don't want bacteria in my grey tanks. I don't even wash food debris (like we do at home) down the sink drain. Or course some gets in, but I wipe with paper towel then wash. Better than that... the greatest invention since sliced bread.... paper plates!
I tend to go into too much detail, but don't mean anything by it... this IS a pretty cr---y subject! If your unit doesn't have one, you might want to "invest" in a black-tank flush valve or cap. I've have used the one that lets you lock it on, then hook a hose to the cap... it lets you fill your black tank... even grey tanks. Before turning on the water don't forget to open the tank valve of the tank you want to fill... or kaboom! This sounds like silly advice, but I've done this several times. It blows off the cap off when "she" can't take anymore... Scotty!
Don't fall victim to this wonderful little prank. Although it has never happened to me (yet), I have heard of some idiot (bless his heart) opens, then closes the black tank valves... knowing what will happen with the RVer removes the cap. So, I always remove the cap slowly so I can screw it back on if I have to!
Back to dumping... like someone said, make sure valves are closed before removing cap... s-l-o-w-l-y. Make sure you always wear gloves when touching sewer things! The sewer cap included. I handle everything else first then sewer things last, WITH gloves. You could have a spray bottle of bleach water handy, but bleach takes a moment or three to work.
I keep sewer things stored in a separate box... which I also use to disinfect / sanitize them in later. Never store them with anything. When dumping at a park, consider everything near the dump station contaminated... not everyone is as considerate as you and I
. After dumping; putting away sewer things, leave the area rinsed off, and after you take off rubber gloves, wash your hands well... sanitizer does not get hands clean!!!
Oh... a good way to clean the ole black tank even better is to leave a little water in the tank (5 gallons or so) then add a little dish-washing detergent to the tank, via the WC and let the drive home do the work. I've heard a couple of bags of ice down the toilet does this too, but ice is for cooling down refreshing beverages.
One last, Oh, if you are still awake! If I stay somewhere for an extended stay, and with full-hookups, after attaching the sewer hose (no, duh!), I leave my grey valves open, but black closed. A day or so before leaving I close the greys so I can use that water to wash out the sewer hose, etc.