There are many variations and specific situations that can occur, but here is a general description and procedure: Iím assuming this door is a sliding glass type, but an atrium, or even single door would be similar. Hopefully this will give you a good idea of what you are getting yourself into, but please read the cautionary notes at the end.
Generally, the best thing to do first is remove the door panels. This will save weight. You donít want a 9í set of atrium doors falling on yourself if you are planning on working alone. If they have hinges, pop the pins and remove the doors. If they are sliders, usually they simply lift off the tracks, but they also may have little brackets located at the top of them which keep them from lifting, thus making it harder for someone to break in. Remove them and the panels should lift fine. At any rate, if you cannot remove all the door panels, it will be best to make sure someone is around to help.
Next, remove the inside molding. Carefully take a razor blade and lightly cut where the molding meets the wall. If you want to try to reuse the molding, do the same where the molding meets the doorframe. This process will break up any paint buildup, which is bonding the molding to the wall, so when the molding is pried off, the wall paint/paper will not tear as much. The inside molding is generally not part of the original door kit, and should remove easily. The outside molding is usually part of the door kit, and is better secured to the doorframe. If paint buildup exists between this molding and the outside of the home, you may want to use the razor in the same way.
At the threshold, there may be screws, you will want to remove them at this time. There may also be screws at the top of the frame. Remove them also. Then, looking from the inside, you should be able to see nails driven through the doorframe and into the frame in the wall built around the doorframe. By slipping the blade of a reciprocating saw into the gap between the doorframe and wall frame, you should be able to cut all the nails on each side. Sometimes nails will have also been used at the top. If they exist, locate them and cut as previously described.
Now the frame should push out from the inside. If not, you may have missed a nail, or additional nails were used at the outside. Some frames have outside nailing strips. You may find that you will need the use of a crowbar and end up breaking up the old frame, so be careful not to destroy outside siding, brickwork, etc. Also, if your house had new siding put on at some recent time, all the exterior window and door frames may have been capped with aluminum when the siding was done. If so, the capping will probably not be salvageable, and will need to be redone. Now, Iím describing the removal of the frame as well as the doors because the easiest replacement procedure includes what they call a pre-hung door, or a door already hinged and mounted in a new frame Thatís the way most single and double door sets come, but there are manufacturers that sell double and triple door panel sets with frames you assemble before installing.
And now, some words of caution:
If none of this is familiar, it would be best to seek professional help. In addition, after you have removed the old door and frame, what you find may really put you in over your head. This is not to belittle your talents, but from what you describe, and what I have experienced, you may have structural problems due to rotted floor joists, termites, you name it. You wonít really know until the old door is out, so an alternative, to doing the whole job yourself is to do the demolition work, then, if you are unsure, seek professional assistance.
Be prepared, however, that your project may exceed a day or weekend, so develop a plan for securely covering the opening should this occur. I would advise having a qualified person look at the opening (after door and frame removed) to determine what may be needed, and therefore would have a sheet of plywood handy, ready to nail over the opening. This will give you more breathing room to analyze the situation and decide the best course of action.