The screen door has had a rough year. Before my departing housemates can get their security deposit back, we (I) need to repair the screen.
I started by pulling out the piping that was holding the old screen into the frame. I got some new screen and cut off a piece that was a few inches larger on all sides.
Mounting the new screen turned out to be way easier than I had expected. You just need to have the special little tool. It looks like a pizza slicer but the blade is wide and has a little channel in it to cradle the piping. While you're rolling the piping into place, you need to gently tug the screen away from the roller to make sure the screen is taught.
After the screen was mounted and looked good, I cut off the excess with a blade.
That was probably the easiest, cheapest and most satisfying home improvement task I've ever taken on. I highly recommend it.