Shell rot is an unfortunately common issue in turtles, even though it's easy to avoid. It begins to develop when semi-aquatic turtles don't get proper basking areas or heating (red ear/yellow belly sliders, map turtles, etc.) or when terrestrial turtles are in too humid or damp environments (box turtles, tortoises, etc.). These environments mean the shell of these turtles never actually get to dry out, allowing this moisture to grow bacteria, causing the shell to rot away.
To begin treating this, firstly ensure you've made note of all the areas with shell rot. These areas are going to be discolored and usually rougher, and maybe even softer. If the shell rot isn't very severe, and isn't deep into the shell, the turtle isn't going to notice the rot.
You're going to need some supplies to get the job done. Most of the items are things you'll already be able to find. Some sort of mild soap that won't bother your turtle will be needed to get started. Remember to avoid getting any soap on the surface of any reptile or amphibian's skin. Secondly, you'll need something to do some light scrubbing -- a soft (unused) toothbrush will be best. The most important item you'll need is something to kill the bacteria. Your best two options are Betadine and Povidone-Iodine. They're both turtle-safe and will get the job done. Don't forget paper towels and you may want some rubber or latex gloves while cleaning.
Let's go ahead and clean the surface. Use your mild soap and a warm toothbrush to softly scrub any areas with shell rot. Your goal is to remove any dirt, algae, etc. that could be covering some of the bacteria, as dirt and algae aren't actually going to ever harm your turtle. Once scrubbed, rinse off all of the soap with water. If you're not sure what water temperature is best, go with cooler temperatures.
Next, dry the area the best you can with a towel or paper towel, as you're going to use the Betadine or Povidone-Iodine next. Keep in mind that both of these chemicals will stain everything and anything it touches, so be careful. Do your best to cover the entire areas (and then some) with the bacteria-killing solution. Use your fingers, a clean toothbrush or paper towel to ensure the chemical is able to soak into every crack and pore in the shell, reaching all of the bacteria. Once every area is covered, let your turtle sit somewhere dry -- where it cannot access water or anything that can be stained. Your best bet for this is something like a dry bathtub, or in your hands. Keep the turtle out for 15-20 minutes so all of the Betadine/Povidone-Iodine has time to dry. At this point, you can put the turtle back into it's normal enclosure, however, it's even better if you can keep the turtle out of water for an even longer period of time. Setting up a warm heat lamp in a dry area for the turtle for a few hours is a good way to speed up the process.
Continue doing this daily, if possible, for a few weeks. By the time a few weeks have passed, the shell rot should be healed. If not, you will probably want to go to professional help at an exotic veterinarian.
BEFORE YOU GO: Do you know why your turtle had shell rot? Ensure you are following trustworthy care guides and supplying your turtle with exactly what they need. Shell rot isn't afraid to come back if you continue neglecting to give your turtle proper UVB, basking, and dry areas in their enclosures, or are creating too damp of an enclosure for terrestrial turtles. Good luck!
SEE THE PROCESS IN THIS GOHERPING VIDEO: