The most cost-effective way to grow basil is to start it from seed in the Spring. This is easy enough, but the seeds do take a little longer to germinate, so start early in February or March at the latest. After they sprout, the seedlings are fragile and will need to be watched carefully. Make sure they are not under- or over-watered.
Seedlings can be transplanted into the garden after all danger of frost is over, or planted in a pot on the windowsill. From here on out, basil is a pretty easy keeper. It will take a few months to get a good-sized plant growing. In the garden, watch the basil for bugs, and also pinch out the top flower buds. This will allow your plant to bush out more, instead of growing tall and leggy and going to seed.
Full-grown plants can also be cloned, or propagated with cuttings. Simply cut a 3-4" piece of stem above a pair of leaf nodes. Set the cutting in a jar of water and wait. After a couple weeks, you will see little roots growing out of the stem. These cuttings can also be replanted in the garden or a windowsill pot after they have grown a decent root system.
I preserve my basil in two ways. You can either make pesto and freeze it in ice cube trays, them transfer the cubes into a plastic baggie (hint- you don't want the pesto exposed to air). This is the same process I use for freezing cilantro, which loses its flavor when dried.
Basil, however, is an herb that CAN be dried as well. I usually thin out and pinch out the tops of my basil plants, then save the tops and thinned parts to dry. These parts are just set on a cookie sheet and put in my gas oven to dry for a day or so. You don't need to turn on a gas oven- the pilot light keeps it warm and dry enough to easily dry most herbs. After the basil is dry enough to crunch, I put it in my Vitamix Dry container to grind/powder it.
Do you grow basil? What is your favorite way to use it?