place the doggie door on the door to be cut, make sure you have the square set on the door where ther is at least 2 inches of material at the bottom. Trace a line around the frame of the doggie door. check on doggie door how far the screws are in from the edge of the frame. then redraw a new square inside the one you just drew in as far as the screws are in (just on the other side of the screws is what you'll need for the screws to be able to go though the hole) ...
on the new smaller square you just drew, drill a 5/8" hole into the corner of the square all the way though the door. Using a small jig saw with the proper blade (wood blade for wood doors, metal blade for steel clad doors) cut the hole out.
insert the outside of the doggie door into the hole (have someone hold this in place for you). then, place the inside of the door into the hole and insert the screws. (these are usually plastic, so use a screw driver to insert the screws not a drill)
total time "1 hour.