For me, this is the most difficult part. You will have to choose what type of basil you want to grow.
Mrs. Burns lemon basil
Water the plants lightly, about twice daily. If you used plastic to cover them, remove it once the plants emerge.
Once the leaves formed your plant can be re-potted or put in the garden. Word of caution. They will die if there is a frost. These are warm loving plants. To plant into the garden pinch off the bottom two leaves, turn the container upside down and gently tap until the plant slides out. Bury roots and stem to cover the spot where the leaves were pinched of. Pat down soil to eliminate air pockets.
Love your plants. I prune the leaves as the plants grow. We always have a fresh supply in the house. One important tip - never let your basil plant flower. Once it does, all the flavor is gone. It is a mean thing to do to the plant, sorry, but remove those flower buds as soon as you see them form.
Enjoy your plants and your pesto.