How do I clean the inside of my toilet tank?

take the lid off; flush the toilet and hold the float up so that it will not refill; if it's gunky reddish brown it's a rust film; wipe off as much as you can with paper towels , then wash with a Vinegar/baking soda paste and a sponge.

I just saw a post on Hometalk today where a guy cleaned his toilet with peroxide. It was a pretty detailed post.

Bi-Carb soda (3 spoons) and white vinegar (1 cup).

My method is only slightly different from Landsharkinnc. I turn off the water valve behind the toilet. Then I flush to empty the tank. I remove the heavy tank lid. I spray vinegar from an empty pump hair spray bottle into the tank, especially over the rusty areas and the workings with vinegar. Then I sprinkle the vinegar areas with baking soda and let it set for half an hour while I do other things. After that, I scrub everything with a toilet bowl brush. I turn the water on and flush. When the tank fills again, I use a sponge to clean any remaining gunk, then flush again. I continue to flush until none of the rust ends up in the bowl. I replace the lid and clean the bowl with vinegar and baking soda. I used to do this once a week. Now I do it rarely. That lid is really heavy! Best wishes ☺️

Thanks, everyone. It sounds like baking soda, and either vinegar or peroxide will do the trick. I appreciate each of you for responding!