This was the easiest mod I have done to my Explorer so far. It took me about 1 hour. And it only cost me about $10 or so. First of all, buy all the supplies at your hardware store. 

You will need:
2 adjustable clevis pins
4-6 washers that fit the clevis pins
4 cotter pins that securely fit clevis pins
Drill with bit the same diameter as cotter pins
Small detail saw
Bungee cords

Rear

Find the connection between the swaybar and the frame. Connection shown below. Unscrew the nut that holds them together. Now you should be able to pull the two pieces apart, but you don't need to do this until you want to disconnect the swaybar. After trying and trying to pull out the bolt that connects the two (and loosing a tooth), I got smart and drilled a hole in the center of the bolt close to the head of the swaybar. Do this with both heads together. It does not have to be too exact because you can fill in the space with extra washers as needed. This hole is to fit the cotter pin.

After both connections are disconnected the swaybar should move freely up and down. Then securely tie up somewhere on the axle with bungee cords. 

Front

First remove the entire bolt holding the swaybar to the axle on both sides. This make be hard and my require a hammer. After bolts are gone, fit your clevis pins into the hole and add washers to the nearest hole for the cotter pin to fit. With both disconnected, the swaybar should move freely. 

I had to cut away some of the wheel well, plastic, to keep the sway bar from interfering with the springs when tied up. Tie up onto the frame with bungee cords, shown below.

Both front and rear takes me about 2-3 minutes to disconnect and about 5 minutes to reattach.

Hint: Make sure car is more or less level, and that makes the process much easier. There are many ways to accomplish this, and some other ways may be better. This is the way I chose and it works very well.