One thing I do that was not mentioned is that I have an inline water meter that attaches to my hose. That way I know exactly how much water I'm putting into my tanks. This is much more accurate than just counting or timing the water input.
As BB-TX above said, drain the black tank until flow stops. Turn on the black tank flush water and watch for solids. When that appears somewhat clear, close the black tank flush valve and add about 10 to 15 gallons of water. Open black tank valve and drain. Knowing the size of your black tank will help as you can nearly fill it with water and flush it to get most all debris and "stuff" out. It should be around 50 gallons. I never add more than 40 to ours when flushing.
After flushing several times, I will close the black tank valve and add about 5 to 7 gallons of water to start the next cycle. I leave this in the tank, don't drain it. Go inside and add your chemicals to the tank for the next cycle. I use Unique RV Digest It, but any chemical you choose to use will need a good amount of water in the tank.
As stated, drain gray tanks to clean out sewer hose and you're done.
The meter is also handy for adding water to the fresh water tank using the "tank fill" option you mentioned above. I usually keep about 10 to 15 gallons in the fresh tank for use when travelling so we can flush the toilet and wash our hands, etc. It's never a good idea to travel with full tanks. Here's some links to what I use...
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1