The best tip I can give is - Don't let your shoes get soaked through.
At WDW, there are plenty of situations with potential for foot-wetting. In late summer there is rain every day, though it's usually for less than an hour. There are play fountains for kids in several locations. And of course, there are some wet rides. But if you pay attention to where you walk and how you walk, you can keep your feet dry.
Stay out of the rain as much as possible.
When the pavement is wet, don't walk through puddles.
When you're walking through a wet area, walk lightly - don't stomp, and don't run - and you won't splash water onto your shoes.
You can't always avoid situations where your shoes will get wet, but when you do encounter those situations, don't just stand there - get out of them as quickly as possible. The less time you're in a wet situation, the less chance the water has of soaking through your shoes.
After your shoes have gotten wet, and you've gotten out of the wet situation, dry them off. Start by stomping them off at the entrance to a building to remove excess, and once your inside, some napkins or paper towels can remove the worst of the water (I seldom need this, however, unless the rain is unbelievably heavy).
If your socks get wet, find a bathroom, take them off, and wring them out the best you can. If you leave the upper parts of your socks wet, the moisture will wick its way down into your shoes.
By following these tips, I've kept my feet dry through over 20 trips to WDW since 1990. I've only had my shoes soak completely through to my feet once or twice, and by drying them immediately, I've never had a water-related foot or footwear problem.