Decide on a style and design. Grill roofs can be permanent or temporary. You can build a small structure, just to cover the grill, or a larger structure to provide some covered seating as well. Design options include simple vinyl or metal pipe structures or built wooden frames, covered with corrugated metal, plexiglass or wood roofing with shingles, perhaps to match the house.
Build a simple grill roof by setting four 8-foot tall, 4-inch-by-4-inch posts two feet deep in holes filled with concrete. Place the posts to create a 6-foot-by-4-foot frame around the grill location. Cut four 2-by-4s (two at six feet and two at four feet). Nail the 2-by-4s to the top of the posts.
Brace the corners with 2-by-4s cut at a 45-degree angle on each end. Nail them to the posts at the bottom of the frame. Attach the frame and braces with 3-inch galvanized screws. Nail or screw pressure-treated plywood or plexiglass roofing to the top of the frame to cap the structure. You can use vinyl or metal pipe to make a similar roof, covered with plexiglass or canvas.
Make a larger grill roof by setting 4-inch-by-4-inch posts in concrete at four corners to make a 4-foot-by-8-foot rectangle. Nail four 2-by-4s--two 4-foot long boards and two 8-foot long boards--in a frame around the tops of the posts. Brace the corners with four 2-by-4s cut at a 45-degree angle on each end. Connect them to the posts at the bottom of the frame with 3-inch galvanized screws.
Nail two additional 4-foot-long 2-by-4s between the outside long frame boards to act as rafters for the roofing. Finish by screwing corrugated metal or plexiglass or nailing pressure-treated plywood or wood planks onto the 2-by-4s to make your roof. You can make a similar framework of vinyl or metal pipe, with corrugated roofing.