Place two of the pickets together, back to back. Use the bevel square to mark a 45-degree angle across the end of the face. Mark another 45-degree line at the other end, so that the short side of both lines are on the same side of the picket. This is referred to as "short point to short point." Cut both along these marks. Set the pickets aside for now.
Place the two pieces of 1-by-6 on a flat surface. Place two pickets on top of these boards, one picket at each of the boards, and flush with those ends. One of the boards should be moved until it is 6 inches from the top of the pickets, and the other placed 6 inches from the bottom. Use the framing square to make small adjustments, and attach the pickets to the 1-by-6-inch boards using 2 3/4-inch wood screws at each board. Make sure that this frame fits your fence opening, and make adjustments to it before going any farther in the construction.
Turn the gate frame so that the two pickets are face down. Place two more pickets at the edges of the material, as before. These will line up exactly with the ones already mounted on the other side of the gate. Space the remaining pickets out evenly across the gate, mounting them to the cross members with one screw per picket per board.
Stand the gate upright so that the bottom of the pickets are all touching the ground. Brace the gate in this position to help you align it for the final braces. Place the two cut pickets on the 1-by material and roll the top piece over. Place the two pieces in the center of the gate so that the form a peak at the edge of the upper 1-by-6-inch board, and reach toward opposite ends of the lower one. Use the framing square a final time to align the gate, and attach the braces with two screws per joint.
Install the hinges so that the gate will be lifted 2 inches off the ground. For the most dependable results, use butterfly hinges with long wings on the gate side. This helps distribute the stress of the weight across a wider area, and offers a stronger hold with less stripping. Install your latch according to the instruction that come with it. There are many types of latches, but most require between two and four screws in both the gate and fence post.