An octagon deck is often associated with outdoor gazebos. However, an eight-sided outdoor platform style wooden patio makes a nice addition to your backyard. That's true even without the overhead roof. The octagon space seems to be a congenial configuration. That gives everyone ample space to move around and enjoy the company of each other. In construction terms, an octagon is nothing more than a modified square. If you keep this geometric concept in mind during the construction process, then your deck should turn out just fine.
Acquire all materials and bring them to the job site. If the platform is twelve feet across or less then you can use 2 X 6's, otherwise you will need a 2 x 8 joist. Cedar or redwood is preferable to pressure treated wood. Overall, you will need eight posts, which will be placed in the ground or set on top of concrete piers. If you cannot find a cut post, then you will have to cut each post at an angle. These are rip cuts that need to run along the length of the post.
Lay out the deck, starting with the location of the upright posts first. The math for this step is really very simple, if you regard an octagon as a square shape with all four corners lopped off. For example if you want to build an octagon deck that is twelve feet across, then first you must lay out a twelve foot square area. Now divide each side into thirds and these marks will be the eight corners for your eight-sided deck. Each mark will be situated 4-feet along the outside perimeter from the corner of your original square. (This is not a perfect octagon, but it is very close in size to one. To get a real octagon you have to do some more advanced math that involves the hypotenuse of a triangle. The simpler version does not change the angle of your cuts and will look almost identical.)
Dig the holes for the post or concrete feet. You can do four piers at a time, to make things easier. Put in place two opposite pairs of posts at a time and things will go smoothly. That means that first you will lay out a rectangle that is 4 feet wide and 12 feet long. It is a good idea to put in temporary diagonal braces at each corner. Use 2 X 4's for this.
Make sure the top of all the posts are level. (Actually a slight slant in one direction is not a bad idea. It helps shed rain water). You can cut a post if you have to, but the idea is to level all posts with out using a cut to make a correction.
Measure and cut the eight-sided box frame that will go around the perimeter of the eight posts. 22 and a half degrees is the magic number here. It is the angle you will subtract from 90 degrees when you cut the end of each board. So set your saw at 67 and a half degrees and start cutting. Do one piece at a time.
Cut and fit the floor joists. Do the ones that are the longest first and gradually work your way out to the edge. All bevelled cuts should be done with your saw again set at 67 and a half degrees. Attach the joists with nails or building screws driven in from each end. The joists should be placed 16 inches on centre.
Finish the frame with another framing member attached to the outside of the box. The end result will be that a double frame that completely around the outside of the octagon.
Cut and fit the floor boards. Do the longer pieces first and cut each end flush with the edge of the frame. Leave a small gap of 1/4 or 1/2 inch between each board. Nail each board with #8 galvanised nails or special decking screws. Run the boards perpendicular to the floor joists.
Apply a sealer or paint finish if necessary.
Work on sawhorses and use safety glasses.