How to convert a door into a window
You need to reframe this opening with a bottom plate, window sill, and cripples.




Remove the existing door and trim all the way back to the header, jack studs, and subfloor.
Install a new bottom plate on the subfloor with a foam weather stripping between to prevent drafts.
Install cripple studs at 16" intervals that continue the stud spacing outside of your window framing. Locate a few studs to either side of the window frame with a stud finder and install the cripples at a continuation of this spacing. You also want one on each end of the sill, screwed into the jack studs. For now, only install the two cripples on each side.
Install the sill on the cripples and screw it to each cripple and into the jack studs. Install the other cripple studs, ensuring that they are plumb and that any bowing is the same direction, preferably bowing out.
Install an exterior sheathing over the new framing. This should be nailed about every 10" or so, more on the edges, and you can get away with smaller nails (I believe we only use 8 penny nails for this).
Install a house wrap moisture barrier (e.g. Tyvek) and use a house wrap tape to seal it to the existing barrier.
Install a rubber seal around the bottom of the window opening. It should overlap on top of the house wrap and extend up each side slightly.
Install the new window. This should be sized for your rough opening, and you should have cut your cripples for the height of this window with an allowance for shimming the window and installing trim. Make sure the window is level and plumb. A new-install window will be screwed into the outside of the house while renovation windows are screwed into the side. I'd go for the new-install style if you have the space after removing the old door frame and trim.
Install a rubber seal around the sides and top of the window starting the sides and then the top plate. You cut the top corners of the house wrap at 45 degree angles. The sides are installed top of the house wrap, but go underneath the cuts in the top corners. The seal goes under the vapor barrier at the top. This ensures that any water behind the siding runs way rather than into the house. Use house wrap tape to seal the cuts and top of the house wrap.
Caulk any cracks or joints. Place insulation into the wall under the window, with a vapor barrier facing inside your home.
Install drywall, mud and tape the seams. It's best if you avoid joints in the corners of the window, which you can do by cutting back the drywall to the next stud on each side.
Install trim and siding on the outside. Caulk the edges and paint. Advice on what type of siding will go best falls into decorating advice (off-topic per the faq).
Install a trim box around the window opening, loosely fill any spaces with insulation, and then install trim between the window box and drywall. Caulk and fill any nail holes.
Sand and paint.