The most cost-effective way to cover a patio often involves using temporary or semi-permanent solutions. Shade sails, for instance, are affordable and easy to install, providing protection from sun and light rain. Another budget-friendly option is a retractable awning, which can be extended when needed and retracted when not in use.
For a more permanent but still economical solution, consider a pergola with a fabric or vinyl cover. This option allows for customization and can be built using relatively inexpensive materials like pressure-treated lumber. Adding a polycarbonate or corrugated plastic roof to the pergola can provide additional protection from the elements while keeping costs down.