Install a hot tub enclosure product. Options include gazebos and domes. Most gazebos and domes require assembly. They consist of frames and panels you must connect.
Set privacy panels around the tub. They come in wood or composite materials. Most can be connected to create a panel wide enough to fit around the tub. Keep one side open for access and position the panels primarily on the sides receiving the most wind.
Consult with a structural engineer to discuss recessed options. If building a new deck, place the deck on a concrete platform and build the deck around it. If cutting into an existing deck, the tub must still sit on a platform to accommodate the tub's weight. The best configuration varies with the deck installation. A structural engineer can identify how to best place the tub while providing the least amount of stress on the decking structure.