I use a balm on my feet every day and I really benefit by it. What you can use is basically any creme/balm that hydrates the skin. A bonus would be the kind that prevents sore feet, so after a day of walking you still wouldn't have painful feet. Basically you'd have to pick what suits you best.
Also make sure your socks are not too tight. Keeping the toenails at a decent length (and definitely not too short) is good advice too.
Do not file away hard skin if you're not absolutely sure it is just that: hard skin. Otherwise, see a professional and let them take care of it.
The balm I mentioned before usually also keeps hard skin away.
Do NOT use feet baths (is that what you call them?). The skin will become too soft and apparently that's risky.
After shower/bath dry your feet well, but don't rub them. Make sure you clean and dry well between the toes. Applying the balm right after a bath or shower is a good idea.
I've seen advice to wear those pool shoes (or whatever they're called) in the shower because of the risk of infection from other people who use the same facility. I'm not sure if I believe in it, but I just thought I'd pass that on as well.
Obviously you are more at risk, so if you share your bed with someone with feet problems, wear socks or any other kind of protection.
Also, wear footwear in the house!
It seems a lot of things to do or not do, but the last thing you want is trouble with your feet. Some things seem overdone to me, but I do follow this regime and my feet are doing great.
Oh, last, but not least: if you see any change in your feet tell your doctor/nurse or specialist. If something is wrong it's best to be on it as soon as possible.