Welcome, blossom22!
The usual substitution is 1 teaspoon dried (chopped or crumbled) dried herb in place of 1 tablespoon fresh. So you would want to use 1/3 cup of dried basil.
HOWEVER: there are uses in which you never want to substitute a dried herb for the fresh one. Pesto, for example -- oh, sure, "they" say you can use dried basil and goose the color with parsley, but really that's not worth making (or eating

). If your recipe relies on the fresh taste and color of the basil, it's better to make something else instead of use dried.
Remember also that dried herbs are usually added to a recipe at a different point from fresh. Because fresh herbs are mostly pretty delicate, they tend to be added near the end of cooking, if not actually after the food has finished cooking. Dried herbs need more time to reconstitute, and so are usually added much earlier in the process.