I wanted a way to let my cat onto our porch, without letting all the cold air in. He loves to sun on the porch, and I wanted to move his litter box out there to free up the closet it had been in. I looked at pet doors a few places, but was not prepared to spend that much. My door is lacking some of the features of the doors I looked at, but they were features I didn't need, and mine was essentially free(since I already had the duct tape). I wanted it to be a two way door, so I didn't need features that let me set it to one way. My porch is enclosed so I don't need to worry about locking it when I am away or to keeping other animals out. The porch is not heated, or even insulated for that matter, so we just needed something to keep the draft out.
I used:
1 8.5x11 sheet of paper
Duct tape

Step 1: Make Sure the Opening Is Pet Safe.

In my case the door to our porch had a broken pane of glass which had been covered with a very classy piece of cardboard for a year. Making the hole pet safe, for me, involved pulling shards of glass from around the edges with pliers.

Step 2: Cover the Paper in Duct Tape

Start covering the paper with the duct tape. When the first side is done, flip it over and do the other side.

Step 3: Adjust the Size

Hold your door up the the window to make sure it is the right size. It should extend past the top and bottom of the hole by a little bit and be not quite as wide as the hole. Mine was too small on all sides, so I added some more duct tape.

Step 4: Make Fringe

Make two strips of fringe, one for each side.
Fold a piece of duct tape the height of your door in half lengthwise.
Cut the edge into fringe. It helps to fold the strips in half so you can cut two layers at once.
The fringe will let the door move more freely.

Step 5: Test It Out

Attach the pieces and see if they are the right size. In this picture the door needs to move to the left.

Step 6: Tape It On

Cover the top and edges with duct tape and you are done.
You can see in the second picture what it looks like when the cat has gone though it. It lets in more of a draft, but when he comes back in it rights itself.
It took us 10 minutes to teach him how to use it, but now he dives through it with no hesitation.
I was going to add magnets to the bottom edge to keep it closed tighter when he is not on the porch, but I haven't tried that yet. I also might remake it with colored Duck Tape at some point so it looks a little nicer.