Check with your local building department to see if you need to procure a permit for this project. Most municipalities don't require permits for adding fencing and screening to a patio, but there are a few that do. If you skip this step and actually needed a permit, you may be required to tear down your work and start over.
Assess your current patio layout. When enclosing the patio with screening, it's best to have support beams every eight feet or closer. If your current support beams are farther apart than eight feet, install more support beams. Try to buy new beams that match the old beams, and cut them exactly the same height. When sliding them into place, put wood shims at the bottom or top to make the fit as tight as possible. Paint the new beams with exterior paint to match the existing beams' paint.
Measure the space between your support beams, and cut two-by-fours to fit between the beams. Lay these lengths of lumber on the floor on the 2-inch side between the support beams, and screw them into the support beams at an angle with 2-inch screws.
Decide how tall you want the fencing to be. Cut your rails to this height, and stand them up next to the two-by-four boards you already screwed to the support beams. Space them evenly by cutting a piece of wood that is the length you want between rails. Use the piece of wood as a guide when placing your fence rails next to each other. Screw each rail in place as you position them.
Attach another two-by-four on the other side of the fence rails on the floor. Attach the second piece of lumber with wood screws to both the rails and the patio support beams. Sandwich the tops of the rails between two more two-by-fours and screw the lengths of lumber to the rails and to the support beams. Paint the fence railing before proceeding to Step 6.
Unroll the patio screening and use a staple gun to staple it to the patio support beams, the ceiling and to the bottom fence support rails. Pull the sheeting tightly without stretching it out of shape. Trim the patio screening with sharp utility scissors.
Cut pieces of quarter round molding to fit along the edges where the screening has been stapled. Paint the quarter round molding before installing it because it's difficult to paint it once it's installed without getting paint on the screening. Install the quarter round molding by attaching it to the patio ceiling, support beams and fence railing with finishing nails.