Screen-frame stock can be purchased in most home centers and is fairly inexpensive.
Begin by cutting the metal frame-stock using a hack saw and miter-box (Image 1). To save time and ensure uniform lengths, you can cut two lengths of stock together at the same time. Cut the equally long top and bottom pieces together, then the two identical side-pieces. The lengths of frame can be cut straight with no need for miter cuts since the corners of the frame are joined together with L-shaped corner clips (Image 2).
In this demonstration, we used fiberglass mesh.
Once you've cut and assembled the frame, you're ready to install the screening wire. Lay the screen mesh over the frame, and use clamps to secure it and hold it flat and tight while you work. If the material has come from a roll and is not perfectly flat, lay it on the screen concave-side down.
The screen is held in the frame by spline material, also available at home stores. Unspool a length of spline and install it by pressing it into the frame's groove using a rolling spline-tool. Gently pull the spline tight with one hand as you carefully press it into the groove with the roller. Be careful not to allow the roller to slip out of the groove as it could damage the screen mesh.
Upon reaching the corners of the frame where the roller won't reach, use a flat-head screwdriver to press the spline into the corner (Image 1) and continue on with the spline tool (Image 2). As the spline goes into the groove, it helps pull the screen taut. Always work in the same direction with the roller -- don't back the wheel up.
When you have installed spline all the way around the frame and come back to the starting point, trim the spline to length using a utility knife. Also use the utility knife to trim off the excess screen mesh from the outside of the frame. Allow the blade to ride along the outside of the frame's groove to ensure a straight, clean cut.