How to clean mold & yuck in the toilet back water tank & how to keep

You can probably put a quart of bleach in the tank about once a month or so. Let it sit overnight and flush in the morning.

http://homeguides.sfgate.com/remove-mold-toilet-tank-42053.html

Susan is correct but calcium hypochlorite, the active ingredient in bleach, is tough on the toilet's working parts. I would say that if you are getting actual mold the toilet isn't being flushed at least once a day. Keeping it active cuts down on a lot of problems.

You might try the old standby, distilled vinegar. After it has some time in the tank, brush everywhere you can with the toilet brush and flush until the water in the bowl is clear.

If you decide to go the bleach route, Clorox and others sell tablets (don't get the dollar store ones, they are useless) that you drop into the tank and they keep everything good for a month or so when you drop another tablet in. They claim no harm but both of my new toilets, Kohler and Glacier Bay, void mechanisms if you use them. Since they use those high-tech computerized (read "expensive to replace") flush and fill mechanisms I am heeding their warning.

Pour about 1 cup of bleach in the tank....let sit at least an hour... scrub out with a brush (like a dish brush) and flush . Repeat if needed, until mold is gone. Be aware that chlorine bleach is hard on the rubber flapper in your toilet tank.... keep a spare on hand.

You can also trade out the bleach for vinegar if you're concerned about harsh chemicals :)

Chlorine bleach will erode rubber over time... it has less effect on seals that are made of composite (more plastic based) material.