You'll have many options for covering an octagon-shaped window, whatever your budget and taste. From sheer curtains softly filtering the light to all-out shuttered darkness, from budget-friendly window film to custom-made cellular shades, your biggest problem might be deciding which alternative you like best.
If you like the look of sheer curtains for your octagon window, buy a flexible rod that attaches to the window frame with a set of clips. You can bend the rod to fit the window, cut it with a hacksaw if it's too long, or add another rod if it's too short. Add a sheer curtain that's long enough to reach the middle of the window. When you attach the rod to the clips, gather the curtain in the center and secure it. Your window is now completely covered by the gathered fabric. You can buy kits for this treatment, known as a "sunburst" design, or buy the rods and supply your own curtain.
Shades and Shutters
Companies that specialize in custom-made window coverings offer cellular shades and shutters made to fit windows of any shape. A cellular shade can be attached to the top of an octagon window and raised to let in light. A shutter can be designed in sections, allowing you to open or close as many sections as you like for light or privacy.
Adhesive window films are available in a variety of patterns, including mirrored and frosted. You can also choose a product designed to reduce the amount of heat or light that enters the room. The film is easy to install. Cut a piece to fit the window, mist the window lightly with water, remove the film from its backing, and press it into place. When you're ready for a change, just pull off the film and replace it.