One other tip for marshwatcher: if you're at a site with full hookups, leave both valves closed (particularly the black) and only dump tanks when you are at least 2/3 full. You want to build up the waste with water and give it a chance to break down a bit, and then when you open the valve when you get near full, you'll get a strong outflow that will carry most/all of the solids away.
If you leave the valve to the black tank open all the time, the liquids will drain off and the solids will collect at the bottom of the tank, eventually forming what is called a "poop pyramid" which is very difficult to get rid of.
Apologies in advance for openly discussing a disgusting subject, but if you don't read and learn, you'll have far more disgusting things to deal directly with.
I agree with those above who state dump black first, then grey.