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Put a knife to the caulk around all trim, interior and exterior. Remove the trim. Cut the nails and screws used to hold the old jamb with a sawzall. Remove the old door and jamb. Clean well the frame opening, especially at the bottom.

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I'd use some 3M rot stabilizer to extend the life of the framing at the bottom of the opening. Run a solid bead of quality sealer on the floor jamb, on each side, interior and exterior.

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Insert new door from outside. Level and plumb accordingly. There's some craft in this and shims are most of the times a requirement. Start with the jamb with the hinges. I could go with extensive details but would make the reading tiresome.

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Once set in, plumb and level and with tentative nails - a gun makes it really easy. I use 3" screws for each hinge, one for each, maybe two for the top hinge. Pay much attention to shimming the jamb. Additional screws go behind weather stripping so they stay concealed. Very important that the frame is shimmed at the strike plate. Countersink to avoid undue pressure.

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Insert regular insulation all around, but not forced in. Add interior trim, headless nails to the brick moulding outside.

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If not sure, I'd hire someone with proven skills. You only install that door once but cringe several times a day of installation is done poorly.

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In one word, you cannot. You can replace the door but that's not what you asked.

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Some European countries insulate doors by installing some leather/vinyl covered insulation resembling the old couches of the 60's in fast food restaurants. It might not be your cup of tee. In some cold areas, they resort to double doors 4" apart, one swinging in, one out.

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A storm door can help but not with good looking entry systems.

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You can get by with purchasing a new fiberglass door slab only - keep the frame. $250-$400 plus installation.