You don't say whether you want to do the inside or outside door handle. I'll give the directions for both.
It's only necessary to remove two phillips head screws to remove or install the outside door handle. Open the door and look at the trailing edge. Tucked in by the rubber door gasket, you'll see the two screws. Take those out, slide the door handle toward the leading edge of the door, and it'll pop right off. To install the new one, just reverse the process. The front screw - the one that can only be accessed by removing the door trim panel - should not be tightened to the point you can't slide the door handle forward.
For the inside door handle, use a small screwdriver and pop the trim piece away from the door armrest that extends up to the handle. Once this is down, you'll see a phillips head screw. Take out that screw, which will also loosen the chrome trim around the handle. Pull the armrest piece out of the way, and the trim piece can be pulled toward the front of the car and out to come away from the handle. At this point you'll have the handle assembly exposed. The screws holding it in place are held in place with locktite, so they'll be difficult to remove, and you need to be careful with the long brass rods connecting it to the latch assembly.