On our site, the measurements of screens are listed by WIDTH first and then HEIGHT, and are measured to the closest 1/16th of an inch.
If you're using your existing screens to measure, always measure to the OUTSIDE edge of the screen frame. Also measure at the corners instead of in the middle because over time sun/heat cause the older screen material to constrict and will slightly bow the edges.
A couple of special notes:
Half Window Screens cover either the bottom half of the window (for a vertical window) or one side of the window (for a horizontal window) and are mainly used for insect protection.
Traditional Window Horizontal Window
Full Window Screens cover the entire window and are typically used for Double Hung Windows and/or Solar Screens. They usually have a crossbar across the screen placed where the two parts of the window meet (called the Meeting Rail). The crossbar adds strength and keeps the screen from bowing in the middle. When measuring for the crossbar, measure from the bottom of the window up.
Window Screen Resource Center
The resources below provide information and articles meant to educate and answer any questions you may have related to window screens.