How can I make an outdoor screen that will withstand high winds?

It's more of how or where you are attacking it to. Where is it going? What is it for?

First, don't attack it.

What are you doing it for. Privacy on a porch in the yard? a little better explanation of what you are trying to achieve would help.

The frame and attachment method plus your local wind conditions will determine how well things stand up to the elements.

Secure top and bottom and you should be in good shape.

Do you mean a screen for a window or a privacy screen?