Measure how much farther you want to extend your patio cover. Mark the corners of the extension and dig down 2 feet. Fill the holes 6 inches deep with gravel. Add 6 inches of cement and allow the cement to dry overnight.
Set 4-by-4 corner support posts into the holes. Fill the holes with cement. Hold a level to the posts and adjust until the bubble in the level is centered and brace the posts with scrap lumber to hold it in position until the cement dries overnight. Firmly butt your scrap lumber against the ground and screw to the posts. Use a drill to insert your screws.
Add framing made of 2-by-6 lumber. Frame around the top of your support posts and to the front of the existing patio covering. Screw through the 2-by-6s and into the posts and patio covering, using galvanized screws, keeping the framing flush with the top of the posts.
Hang joist hangers on your framing. Screw the joist hangers into the framing, running from the current patio covering to the framing opposite it. Install joist hangers with a 12- to 16-inch gap in between the hangers.
Install your joists. Hang 2-by-4s in your joist hangers. Screw through the holes in the joist hangers and into the 2-by-4s to secure them in place.
Lay your shade cloth over the joists, allowing the excess cloth to hang over the sides of your structure. Staple the shade cloth to the framing, starting at the corner of the framing closest to your house. Staple the shade cloth into position, pulling it to remove wrinkles and ripples. Use a staple every 10 to 12 inches.
Secure the shade cloth into position, stapling down one side and then the other, always pulling the fabric taut to remove wrinkles. Staple the final edge in place and cut the excess shade cloth with a utility knife.