STEP ONE
For me, this is the most difficult part. You will have to choose what type of basil you want to grow.
Here is a short list of some basil varieties. Click on any of the varieties, I linked online stores where you can buy them.
Licorice basil
Mrs. Burns lemon basil
Spice Basil
STEP TWO
Start seeds in flats filled with equal parts of perlite, vermiculite and peat. Press the soil enough to eliminate any air pockets, then dampen the soil. Drop a couple of seeds into each container, lightly cover them with soil. Wrap plastic around the seedlings and put them in a bright area. If you have a light system in place, that is even better. I live in Seattle, and it is always dark but the kitchen light is usually on. I keep my seedlings on top of the cupboards near the lights.
STEP THREE
Water the plants lightly, about twice daily. If you used plastic to cover them, remove it once the plants emerge.
STEP FOUR
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.
STEP FIVE
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.