I will assume your new door has been measured and is the correct size to
fit in your opening. If by chance the house has settled drastically and the
existing door was cut to fit a largely irregular opening, It may be wise to
use a knock down door made of wood so that it can be cut and built to fit.
For this example however, we are using a prehung unit.

Removing the trim:

Using a sharp utility knife carefully score the paint and caulking where the
interior trim meets the wall and door jamb. This is for ease of removal and
will cause the least amount of damage to the remaining paint as possible.
If reusing the trim, begin at a top corner of the trim and using a flat pry
bar, carefully drive the bar behind the intersection where the top and side
piece join. Pry both pieces at the same time in case the corner is fastened
together. If the trim is overly secured, instead of damaging the wall placing
a wood shim or some 1/4" plywood under the pry bar will help. Work the
trim off evenly around the door. If the bottom of the trim extends excessively
below the top of the flooring were it might break, either cut the lower nails
or cut the bottom of the trim flush to the flooring being carefull to protect
the floor. On the other hand if your not reusing the same trim, after scoring
with the knife rip it off the wall while still being carefull to protect the
wall surface.

Removing the door:

Check for the presence of security wiring by looking for a plastic plug
installed somewhere along the jamb. If found, pull it out and remove it at its
splice. Then remove the magnetic plug on the door. Also check for the presence
of a door bell mounted on the outside trim near the door jamb. If either exist
be carefull when you cut near them. Using the knife again, score between whatever
outside trim there is and the door jamb. Assuming the outside trim does not need
to be replaced that is. Check to see if any screws were used to secure the old jamb
in the opening including any long screw extending through a hinge and fastens into
the framing and remove them. Use a reciprocating saw with a metal cutting blade and
cut any nails or screws still remaining that may be holding the jamb. It will help
to use the pry bar and pry the jamb away from the framing just enough to allow for
access of the metel cutting blade. Usually fasteners are installed on the sides only.
However on occasion I have found them on the head jamb as well. Now take your flat pry
bar and separate the jamb from the exterior trim enough to cut those nails with
the saw. Close the door and pull the door as a unit towards the interior. If the
top of the door will not tilt in without being wedged against the header, Pull the
door from the jamb, cut the side jambs in half and fold the frame in towards the
center to remove.

Installing the new prehung door

Clear the opening of shims, nails or partially cut nails and debris. Clean the new
door jamb of any packaging material, retainer pieces or corner and edge protectors
and their fasteners. Slip the new door in the opening and check its fit including
the margin between the door and jamb on the interior side. Open the door and
support it by placing a block of wood under it. Go on the outside and check the
margin around the jamb and trim and check the door for being relatively plumb.
If all is well remove the door and drill a hole for the magnetic button if a security
wire was installed. Then apply a zig-zag bead of adheasive where the threshold
will sit. Reinstall the door and reinstall the wood block to support it. Shim between
the jamb and the framing behind the top hinge to achieve an equal margin around
the exterior trim. Remove a screw from the top hinge if necessary, preferably one
nearest to the center on the jamb, and while holding the jamb tight to the exterior
trim, drive a 2-1/2" to 3" screw through the hole in the hinge on through and into the
framing beyond. This will hold the door while you double check all margins inside
and out. A shim may be placed under the right or left jamb to improve the margin at
the top of the door, however moving the threshold to the left or right may work as
well without effecting the margin around the exterior too much. Now add shims and
screw at the center and bottom hinges as well and finally near the top and bottom of
the opposite jamb. At the latch a long piece of plywood extending several inches
above the dead bolt and several inches below the knob should be installed. Smaller
shims may be used here for fine adjustments however. When installing your locksets,
secure the strike plates with long screws through this plywood shim and into the
framing.