Take the door out of the door frame by removing the hinge pins, separating the hinges and lifting out the door.
Remove the door frame from the rough opening. How you do this will depend on what kind of door you have. If you are not planning to reuse the door frame, the easiest way to take it out is to cut through one side of it with a reciprocating saw and pry the two halves of that side out, then pull the rest of it out with a crowbar.
Measure the new dimensions of your doorway on the outside wall and mark them with a pencil or a marker. Depending on the color and texture of your siding, a marker may show up better than a pencil.
Cut through the siding with a reciprocating saw.
Measure for the same dimensions on the inside walls. Cut away the drywall with a sharp utility knife.
Cut away any studs that remain in the opening that you have created.
Install a header over the new opening. The header can be made of two 2-by-10-inch pieces of lumber nailed together. The header needs to be supported on each end by two studs.