To make polenta without a pressure cooker, use 2 cups broth and 1 cup water. Bring liquids to a boil in a heavy, deep saucepan, and slowly stir in polenta, garlic, and basil. Reduce heat and simmer gently, stirring frequently to prevent sticking, until very thick (about 30 minutes). (Be careful and use a long-handled spoon because mixture can bubble and spit hot corn meal on your hand.) Add salt to taste and keep warm until ready to serve.
Also note: These polenta instructions are for cooking coarse polenta, not instant or quick-cooking grits. If you are using one of those products, follow the liquid/polenta ratio and times on the package.