First thing I do is put the nozzle of a water hose into the fill and run water until the tank overflows. Then I let it run until no more 'gunk' overflows. Now I pump out some water using the washdown or sink and add some bleach. An ounce for every 10 gallons of capacity , sometimes less, sometimes more depending on how moldy the tank was. Fill with water and let sit for 15 minutes or so. Run the faucets again to bleach out the lines and fixtures.
When the mixture is all pumped out, check any filters or screens and clean as needed. (If a screen is really clogged up, you may have to clean it first before the tank flushing).
It will help a lot to add a bit of bleach to the tank especially if fresh water doesn't get used up very quickly. A small amount per tank (maybe 1/2 ounce/ 10 gal) will keep growth way down.
Of course, don't drink the water and be careful with the water that you drain out when flushing. The bleach can damage your clothes and upholstery.