1995 Ford Explorer exterior door handle

The first part is to remove the door panel. It's held in by the two screws just above the inside door handle, and about 8 of the plastic anchors.
Once you have the door panel off, you'll want to remove the one bolt which holds in the "outer" window tract and move it out of the way.
With this out of the way, you'll be able to see where the linkage between the door handle and the latch mechanism meet. You'll want to detatch the linkage from the latch mechanism by "unclipping" the yellow fastener that holds them together. You'll want to pull the tab on the fastener toward you. Once it's open, be sure to mark the linkage with a permanent marker indicating where it rests in the fastener.
Now you'll be able to rotate the linkage so that it "unhooks" from the door handle.
Now, with that linkage disconnected, you'll need to drill out the rivets which fasten the door handle to the door. You can do this by holding the door handle up, and drilling from outside.
Once you've drilled out the front side, you may need to get into the inside of the door, and "finish off" the rivets from the back. The way these are designed, the rivet pulls into a sleeve, and on the inside of the door, it looks like a banana peel. You may need to bend, or cut off the banana peel parts in order to pull the rivets out from the front side of the door.
Once the rivets are out completely, you should be able to pull the whole door handle assembly upward, then rotate the bottom of the assembly upward, and pull the handle out.