Drying basil is very simple, and there are several tried and true methods for doing it. The first is to merely hang it in bundles. This does tend to discolor the basil so you should place a thin layer of stripped leaves in between two folded sheets of newspaper. You can then hang it on a wire rack and turn it twice a day until completely dry. The paper will reduce the discoloration and oxidation that it would go through without the paper. Some basil lovers like to dry their herb on a special basil-drying screen and then finish the process by baking it in the oven.
When you are drying basil in the oven you should first remove all the stems from the plant leaves. Then, after tearing the basil leaves into tiny pieces, you can lay the pieces on a baking sheet. The oven should be no higher than 350 degrees to reduce the risk of browning. It should take approximately 7 - 10 for the leaves the thoroughly dry, but it may take less time in electric ovens. You should bake them until they are crumbly, but take them out before they turn brown. If this happens you won't be able to use the basil because of the burnt taste it may have. Once your basil has cooled you want to crumble it up more in order to refine it to how you like it. Another way is to use a sieve to help to thin out the basil leaves.
Taken from http://www.basilguide.com/