A birdsmouth joint is the perfect joint to use when making octagonal columns. The birdsmouth joint allows the wood to fit together tightly and strongly. In fact, the birdsmouth joint was used by shipbuilders when they constructed masts.
Angle the blade of your table saw at 45 degrees when you prepare to cut a birdsmouth joint.
Position the fence of your table saw so that the board will be almost the board's width away when you cut a birdsmouth joint. This way, you will save yourself the possibility of the waste getting trapped between the board you are cutting and the table saw's fence, thus kicking back in a dangerous fashion.
Take your first board and guide it along the fence until you are able to get the depth you wish. This depth will depend on the thickness of the boards and the column you are building. You will find that the depth of the blade will match the board's thickness.
Repeat the process with the rest of the boards.
Turn the first board over and place it on the table saw.
Adjust the blade downwards about halfway, and adjust the fence of the table saw 6 mm (1/4 inch) to the left.
Cut the board again, moving the fence to the left as you cut. Continue doing this until the bottom of the birdsmouth joint, or the bird's beak, is flat.
Continue doing the same with all of the boards when cutting birdsmouth joints.