Inspect the doorway with a carpenter's level. Check the floor and the sides for horizontal and vertical straightness. If these surfaces are not level, make a mental note.
Caulk the bottom of the doorway. Start at a point on one side of the doorway, about 1 inch from the outside edge and 3 inches from the floor. Work down to and across the floor, and then 3 inches up the other side. Put down a matching bead of caulk 1 inch from the inside edge of the doorway.
Set the pre-hung door frame and door into the doorway at an angle, bottom first. Push the door kit up into the doorway.
Hammer wood shims under the door frame with a rubber mallet. If the doorway flooring isn't level, drive extra shims to one side to even it out. Check the door sill with a level to track your progress.
Install more shims into the space between the doorway and the hinged side of the door frame. Make any adjustments needed to make the door jamb on that side plumb (vertically level) with shim placement. Also target the area under the hinges for shims.
Fasten the hinged door jamb to the doorway by hammering finishing nails through the jamb near the hinges. Leave the top of the nails exposed, since this is a temporary step.
Step outside and close the door. Inspect the gap between the door and the frame's weatherstripping on the knob side of the door. If the door is not in even contact with the weatherstripping, hammer in shims on that side to adjust the fit.
Step back inside the house and close the door behind you. On this side of the door knob end of the door and frame, a roughly 1/8-inch gap should be between the door and frame. Drive shims behind where the knob and lock will eventually go, as well as any other shims that are needed to ensure that even, 1/8-inch gap.
Open and close the door again, to ensure everything runs smoothly.
Fasten the door frame permanently by drilling holes and installing screws as directed by the pre-hung door kit's instructions, adjusting placement as necessary so your screws go through wood shims and not spots without shims.
Remove the nails from Step 6 with the clawed end of your hammer. Hang the door frame's trim, following the kit's instructions.