Measure your gate opening and plan your gate style. If it is in a fence and you already have posts on each side of the gate opening, that measurement is determined. If you're building a stand-alone gate, say between two rows of hedge, or just starting your fencing, determine how wide you want your gate. In either case, allow an extra inch or inch-and-a-half for hardware. Then decide how tall you want it and how you want to face it -- the bigger it is and the more face boards it has, the heavier it will be. Allow at least four inches of clearance at the bottom.
Set your side posts, if there are none already in place. For a really light gate, you could use 2 by 4s, but 4 by 4s will be sturdier. Dig post holes, at least 18 inches deep but preferably about a third of the planned height of your gate. Set your posts in concrete -- you can mix concrete and pour it wet around the posts or fill the hole around the post with dry concrete mix and then water it in. In either case, make sure the posts are the proper height and are plumb on all sides. If you have to set posts, you'll have to let the concrete dry at least overnight.
Buy your lumber and build your basic gate frame. Generally this means using 2 by 4 boards to make a rectangular frame, to the full width but not necessarily the full height, since facing boards can extend above the top of the frame. It's best to miter your corners, but you can use butt joints if you prefer. In either case, nail or screw them in place and add metal corner braces for extra strength. Or you can add wooden diagonal braces. For a really lightweight fence, use 2 by 2s for the outer frame and use mitered 1 by 4s for bracing in an X pattern. Pine will be the cheapest and lightest lumber but you can use fir, cedar, redwood or other light wood.
Face your gate. You can use 1 by 4 lumber, with plain or cathedral tops, nailed flush or with 1- or 2-inch gaps between boards. You can use quarter-inch plywood and cut a design into it or add a decorative element on the outside. This will depend on how the gate relates to the rest of the fence, yard and house and on how light you want to make your gate.
Install the hinges and latches. There are many varieties, and your personal preference will determine the choice. But get sturdy gate hinges capable of supporting the gate weight and allowing it to swing freely. You can use simple latches or stronger ones that you can lock. Just make sure all hardware is rust-resistant. Screw your hinges to your gate first, then to the post -- many come with hinge pins that you can remove while attaching plates, and then reinsert to hold the gate. (Even with a light gate, this likely will be a two-person task.)