Many fresh herbs can be dried very easily. Thyme, sage, parsley, and oregano are among the herbs that I’ve simply snipped branches off, tied in small bundles, and hung in the kitchen as they dried.
My experience is that basil requires just a little more effort to keep the leaves brighter as well as more pungent.
The best way to dry basil is to cut largish branches and fill a large sized paper grocery bag. Then fold over the top, keeping the basil in the dark, as much as possible, but still allowing for some air circulation. Basil dried in the dark will keep more of its color and flavor.
When the basil is fully dry, it’s easy to crumble the leaves over a cookie sheet or large piece of plain paper. Store the basil in jars to keep it fragrant.