Draw the gazebo dimensions and shape so you can design and construct basic framework for the roof. Cut the framework for the roof from 2-by-6-inch cedar boards using a circular saw, as one option. Buy boards in 12-foot lengths, so you can build a rafter from a single board with the least amount of wasted wood. Use a reciprocating saw to cut the end of each board at a 45-degree angle to reduce some of the bulkiness of the exposed boards.
Install the 2-by-6-inch boards to fit a header beam running the length of a 12-foot-long rectangular gazebo. Connect the roofing framework with bolts instead of screws to withstand strong winds. Bolt the boards together in a pie-shaped pattern if the gazebo is a hexagon shape to form an umbrella-type framework. Predrill holes for the bolts with an electric drill.
Connect the basic framework of the roof cover with 2-by-2-inch cedar strips. Join the rafters cross-wise with 4-inch gaps between them. Secure the strips in place with nails or screws to form a visually appealing see-through roof.
Attach roof framework to support posts for the gazebo with metal connectors or L-shaped brackets that do not show from the yard view. Place these brackets inside the structure after painting them with copper metal paint, so their basic stainless steel color does not show. Drive 4-inch screws into the brackets with an electric screwdriver.
Nail wooden lattice over the edges of the gazebo after painting or staining it. Apply a stain or paint that matches the lattice or trim used on other parts of the structure. Cut the lattice with a jigsaw, taking care not to splinter it. Cover any raw edges with exterior-grade wooden trim to hide them.