Open the door and unscrew the screws holding the door handle together 1/2-inch at a time. Removing the screws in this manner will minimize the amount of binding that occurs when the handles on either side of the door misalign. Pull each screw out of its respective hole.
Hold the door handles tight to the door and then twist one of the handles as if you were opening the door. At the end of the twist pull the handles apart and watch as they come free of each other. The twisting aligns an unlocking mechanism on the door handle spindle so that the two handles can be pulled apart. If the alignment is off the two handles will not separate.
Remove the two screws from the door latch. These screws hold a plate that holds the latch in place. Remove the plate. You may have to pry the plate a little with the tip of the screwdriver.
Slide the end of the screwdriver through the door latch where the spindle of the door handle was removed so that it extends out the other side of the door. Grip the handle of the screwdriver in one hand and the tip of the screwdriver in the other. Face the edge of the door and pull on both ends of the screwdriver until the door latch pops out of the latch hole.