These are some of the little basil seedlings growing in our greenhouse. I've talked to loads of people who seem to have trouble with basil. They plant it out in their herb garden or kitchen garden, and find that it never gets very big or bushy. The key to its success is pinch pinch pinching. Even at this very young age, we pinch off the top. No scissors or clippers required, the growing tip is easily removed with just your fingernails.
Right below your pinch point, the basil will send out two new shoots. This starts the branching process. Once the two new shoots get bigger, you can then pinch the tops off of those. Four new shoots will then sprout, two from each pinch point. Repeat the process continuously throughout the season. Eventually, the basil will send up some fledgling flower spikes. It's imperative you immediately remove those as well. If you don't, the basil "senses" that it has fulfilled its biological destiny, which is reproduction. It then stops growing, and dies.
You see, basil is an annual plant. It has a short life span, just the warm part of the year. Here in coastal central California, we start the seeds on a heat mat in our greenhouse in late January. We then separate the tiny plants into larger pots about a month later. Shortly thereafter, we start to pinch. Since our last frost will be sometime in April, we will wait until after May 1st to transplant these babies out into our herb garden. But we still get the taste of summer now, as the pinched tops don't go to waste. We will take these precious handfuls into the house, and throw them into a pasta sauce, or even the quick and dirty quesadillas we often make for lunch.