The top and bottom of my tortoise's shell tend to get messy from wet substrate, waste, etc. How can I safely clean the shell, without damaging it in any way?
I was afraid of damaging the shell (particularly in the growth regions) by scrubbing at it, so the tortoise's vet recommended using something like baby shampoo.
Baby shampoo has had some unfavorable press in the last few years due to additives. However, most of these additives have been removed from the formulations, and it also uses mild surfactants instead of soap. Surfactants are safer than soap to use in the growth regions in between the scutes (plates) of the shell, because these regions can dry out with regular soap, causing cracking and disturbing the natural "growth rings".
Using a soft cloth or chamois to gently wipe the surface and rinsing the tortoise well to get rid of any residue will remove most of the surface dirt.
There is a good guide for bathing tortoises here.
All you really need to clean a tortoise's shell is water and a gentle scrubbing device of some kind, like a toothbrush or washcloth. Scrubbing (provided it's gentle) will not damage the shell and on the contrary can promote healthy shell growth.
Fill a container with lukewarm water so that it covers the entire plastron, and a few centimetres of the carapace. Let him soak for 15-20 minutes. This allows him to rehydrate and also softens any hardened dirt.
Replace with fresh water and gently scrub him all over, paying special attention to any problem areas, and rinse well at the end. Be extra gentle when dealing with any non-scaled areas, as they will be more sensitive. Coarse salt can be used as an "exfoliator" on any problem patches (shell only, not skin) but should not be used liberally and should be thoroughly rinsed off. If you find your tortoise has a lot of dirty patches that are hard to clean, it could be a sign that you need to clean his habitat more often.
A monthly bathing ritual can be a nice bonding opportunity, keeps the tortoise happy and healthy and also gives you a chance to thoroughly examine your tortoise's skin and shell, noticing problems as soon as they occur. Even when your tortoise appears clean, a regular scrub can remove dead cells and encourage healthy shell growth.
Never clean your tortoise with oil - a build up of oil is harmful to a tortoise's shell, because it can clog the pores. Tortoises "breathe" through their shells as we do through our skin and a buildup of dirt or oil can block oxygen transfer and create other problems. Detergents, shampoos, or other "products" should not be used unless recommended by your veterinary surgeon.