You can fix a broken screen on your window or door very easily. If you’re dealing with wire screens, they’re very durable and can be patched in ways that don’t compromise their integrity that much. Vinyl screens are cheap and much harder to repair. You can still do some simple fixes on them, however, that provide at least temporary benefits. On wire screens, your options are broader. You can fix a broken screen using other pieces of screen in much the same way that you’d patch fabric.
For a wire screen, cut a patch a bit larger than the size of the tear in your broken screen. At the edges of your patch, you’ll notice that straight pieces of wire will stick out a bit. All you have to do to patch most holes is to lay the patch across the hole in the broken screen with some of the straight pieces of metal at the edges of the patch sticking through the broken screen. Bend them over to hold the patch in place. The wire creates an effective bond to the broken screen and the patch will be enough to keep bugs and other nuisances out of your house.
For a broken screen made out of vinyl, you’re usually better off just replacing the entire screen. A broken screen made of this soft material tends to tear very easily if you put any pressure on it but, if you remove it from the window, you can try to lay a patch of screen across the hole. You can hold the patch to the broken screen with glue. Most hardware stores have construction-grade adhesives that will work for this.