Let the Light In
Enjoy your privacy while letting the light shine through with Plexiglas or other translucent plastic paneling. Use white panels approximately 1/4-inch thick for strength and have them cut to the right height, then attach them to wooden posts to hold them upright around your patio. To allow a little more light in, you can also use clear panels and coat them with an adhesive frosted film or spray-on window frost. This will lessen the privacy somewhat, as those outside the fence will be able to see diffused shapes and movement, but may be enough for your needs.
Bamboo and Reeds
Bamboo and reed fences or screens generally come in rolls of the cut plant strung together with wire. These fences provide a warm, natural screen for your patio and can be attached to patio roof posts or new posts added specifically for the fencing. Many bamboo and reed screens do not provide absolute privacy, as there are small gaps between each reed or bamboo stalk, but they do let light and air pass through. To add more privacy to this type of screen, consider planting hedges or using potted plants outside the screen to create additional blockage to the view while still allowing airflow through the area. You can also weave ribbons through the gaps to add decor and ensure privacy---just be sure the colors are weatherproof if the fence is not under shelter.
Wooden fence panels are often available premade from lumber and hardware stores. These panels are generally 6 feet high by 6 feet wide and come in a variety of styles and wood types. Cedar is a good choice for patios with hot tubs or in damp areas because it is naturally resistant to decay. A solid wood fence will ensure privacy, but will also block light and air flow. If you have a covered porch, lighting will be a concern and you may want to attach electric lighting to the inside of the fence. Air flow can be maximized by staggering panels so they are approximately 1 foot apart in depth but also overlap horizontally at least a foot on each side to hide the view. For example, you might align the first panel with the corner of your house along the edge of your patio, then place the second panel 1 foot in from the edge of the patio and set its starting edge 1 foot before the first panel ends.