I may be repeating what others have said, but here goes....
START WALKING NOW!!!
Start with at least 1 mile per day and increase by about 1/4 mi. every 3-5 days. Mostly flat surfaces are okay, since most of WDW is flat, but some hilly terrain would be helpful. Walk briskly... remember, you are trying to increase your stamina and endurance... this is no "walk in the park"

so to speak!! Walk briskly enough to be breathing a bit heavily, but still able to hold a conversation. ANYONE who will be on this trip with you should be doing the same.
Before our last trip to WDW I had been exercising regularly for many months before, but I STILL made sure to be walking a few miles a day for the weeks leading up to the trip and I made sure my kids and DH came along whenever possible.
If it helps, picture yourself walking through WDW. If you know the parks well enough, you can do it by memory (this is how I do it, especially with the MK). If not, find a copy of a park map (maybe google it??) and "walk" through the park. I picture myself walking from the front gate at MK, down Main Street to the castle and then on to other rides/attractions. Then I imagine that I am hustling back to a ride on the other side of the park to pick up Fastpasses, and then back to another ride to meet my family. I keep picture the rides and buildings that I am passing along the way. I try to imagine the music and smells and sounds. It sounds a bit silly, but it really inspires me to keep moving. It is my version of a "virtual visit" to the parks!
My last suggestion is to buy your new "trip shoes" ahead of time and wear them for the last few weeks of your walking program to be SURE that they are comfortable and broken in. It won't matter how much endurance and stamina you have, if your feet are covered in blisters!
Have a wonderful trip and enjoy the "happiest exercise on earth"!!................P