Stick a garden hose into the fill port and fill till it overflows. Let it run that way for several minutes. That will help loosen up gunk and make it float out the filler ( The water hose should be loose and not sealing the opening).
You may have in line filter in your plumbing, somewhere between the tank and the fresh water pump. These filters are often just a fine mesh screen in a clear housing. If you find one it should be cleaned as part of regular maintenance'
There is no easy way to drain the tank except by running a faucet until the tank is drained. That can take a while. All water tanks will grow gunk over time and faster in warm climates.
You can add 1/2 cup of bleach to every 10 gallons of water. Again, don't drink the water and be aware it may bleach your clothes. I don't add bleach, I just every now and then fill the tank to overflow to flush out the gunk.
Note that gunk in the water supply may clog the strainer in your sink faucet and/or other water fixtures like deck fresh water spray.
Finally, if you live in an area where temps go below freezing, you need to winterize the system. That is another topic.