I made a screen door last year, I started by Googling fly screen which iead me to 'The fly screen queen' I then ordered some fine mesh material ( Rayon, I think) it arrived in about 2 days.
I made up a wooden frame with a cross piece 1/2 way and joined it all together using ' L ' shaped brackets for the corners and ' T ' brackets for the middle section.
Next step was to cut the material to length and attach it to the frame using a heavy duty staple gun.
Now came the time to fix it to the outside of the door frame, obviously it needed to open the opposite way fron the door, Ithen fitted a ' D ' shaped handle on the middle bit and the upright which helped with the strength of fhe frame.
The hinges I chose was the kind that you can remove the central pin, this makes it easy if you want to store it away for the winter.
It all worked fine til my german shepherd dog spotted a squirrel outside and ran straight through it ! but luckily it was easy enough to repair. Good Luck with it Tbird+