I recently began a new woodworking project that incorporates hexagons into its design. In fact, there's not a single 90° angle in the entire project - it's all 30° and 60° angles, with some angles being compounded (60° but on a 30° slope). Here's how I approached building the three flat hexagons that are the basis for the project.
First I began by making lap joints for the hexagon. A lap joint is essentially removing the top half of one piece of wood and the bottom half of the other where they intersect. For right angles, this is fairly straightforward, but for irregular angles it's a bit more tricky. I used a dado blade set on my table saw with an Incra Miter Gauge which is precise to 1/10th of a degree.
I set the miter gauge at 60° and set my stop to the precise location so the left edge of the dado blade intersected exactly at the corner of the stock. You can see how a triangle piece of stock was removed in the photo above. It was important to start the dado blade low and slowly raise it, testing with two pieces of wood until they 'stacked' with no vertical excess. Once this happened, I knew I had the correct height for the dado blade. Running the six edge pieces through the dado blade on each end gave me the correct assembly for the hexagon.
The pieces fit together perfectly! Some might say the inner triangle is undesirable, but I actually kind of like it.
I built three hexagons in total. The two smaller ones above are for the top and bottom, and the middle one is roughly twice as big in diameter. This takes care of all the horizontal pieces in the design.
The next steps are to figure out the compound angles for the vertical pieces, which I've temporarily stacked so you can see the overall design (note the middle 'shelf' is missing in these photos). Once completed, it'll be a 14-sided shape that will look like a hexagon from the top, front, and side!