I replaced the brake booster in the sister car, the Mazda Tribute, this weekend. I believe the process is the same for at least the 2001-2004 models, whether Tribute or Ford Escape, since they use the same engine.
Just a few observations.
1. While you obviously need to unbolt the master brake cylinder from the brake booster, I was able to remove the brake booster WITHOUT disconnecting the metal master brake cylinder brake lines (which would have required me to bleed the brakes if I had disconnected the master brake cylinder).
2. If you go this route, be sure to disconnect the wire sensor plug that attaches to the master cylinder. There is small clip on the top of the plug (mine was colored red) and it slides out completely (make sure not to drop it into the engine), and once that small clip has been slid out, the plug can be removed from the master brake cylinder. If you don't remove this wire sensor plug, you risk braking the plug or wire, since you will need to push this entire assembly down and to the left when pulling out the brake booster, and the wire is too short for movement in that direction and will possibly snap.
3. The vacuum hose should also be removed before trying to pull out the brake booster. You don't need to undo any of the clamps on the vacuum hose, just simply pull it out from the brake booster (it is intended to be simply pulled out when removed and simply pushed in when installing).
4. I needed a deep socket (13MM) to remove most of the nuts since the studs onto which the nuts are threaded extend sufficiently past the nuts that a shallow socket will not reach them.
5. It took some contortions to remove it from the clutter of the surrounding pipes and wires, but it worked by pulling and turning the brake booster (once separated from the master brake cylinder) all the way to the right (toward driver's mirror) and slightly upward, in order to clear the brake booster's long push rod (that extends into the driver foot well) from the firewall cutout. Once the push rod had cleared the firewall cutout (the booster was still caught in the engine compartment), I rotated the entire assembly almost 180 degrees so that the push rod was now facing the front of the vehicle. The entire assembly could then be lifted out of the engine bay.
6. Make sure the actuating rod in the replacement brake booster is set to the same distance as the one you are removing.
7. When disconnecting the brake pedal from the inside of the car at that point where it attaches to the push rod of the brake booster, remember that there are two white plastic washers on either side of the brake pedal spindle, as well as a black plastic bushing (this will all be obvious when disconnecting these parts, nothing complicated here.
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) and you will have to replace it, and bleed the whole system. so, be careful 
