For saving seed with basil see the link below. Of note, you'll only want to save seed if you are growing a variety that is NOT a hybrid. Seed from hybrid plants do not come true.

FataMorgana

Here is a link that might be useful: Google - Seed Saving - basil

You won't have to worry about a lot of basil seedlings sprouting up all over your garden. The seeds stay on the plant and do not broad-cast themselves. They can even winter over staying on the plant. If you have more than one plant you let one go to seed and use the rest. I plant sweet basil from seeds then the next year I use the seeds from one plant. The seeds you save are more viable than those you buy so I try to save one plant each year for seed the next. I don't even bother to do anything except pull the seeds off the dried plant and save them in any envelope until the following spring.
Paul