How do I make my old screen door look new?

Hi Gloria, take a wire brush to your door and get all the loose paint off of it that you can. Then I would use an oil based paint to repaint it. Rustoleum has always been my go-to even on wood for a lasting paint finish for exteriors.

Here's a tutorial on a wood door, which may be what your door is made of? https://www.youtube.com/watch?v=4kCsMhBDAEU

Scrape old paint and then spray paint after cleaning. Use a good door paint.

Gloria....You may need to replace screen too.