When the basil in my backyard starts getting leggy, I pinch off the purple flowers and...
about 1/3 of the length of the plant, and it comes back bushier than ever. If it were me, I'd move yours outside. But I don't know your particular circumstances, and if that's what you want to do. Never grew any herbs inside, myself.
I don't know if it will winter over where you are (down south?), but in NYS, outside, it's the first victim of the first frost ;o) Turns black immediately.
I never water mine, let the rain take care of it. I do know it likes a lot of sun, and I suppose if we had a real hot spell and it started looking droopy, I'd probably water it a little bit once a week or so.
Hope that helps.