According to my garden books, celery needs rich soil, regular water, and liquid fertilizer every two to three weeks. It likes long periods of warmth but not high heat... that means if your summers get above 95 degrees F, you would probaly do better to grow celery as a spring or fall crop. It's slow to get started, so most people probably buy seedlings; the garden books recommended that.
Celery, being a heavy plant, tends to fall over, so most people hill it up (heap soil around the base) as it grows. This also gives you white bases. If you wish the stalks to be white farther up, you can wrap them with a bottomless milk carton or something similar, but be sure the leaves still get sunlight, and allow for the plant to expand as it grows.
If you are an organic gardener and don't wish to use chemical fertilizers, you can use fish or seaweed emulsion or compost tea as the liquid fertilizer. You can also dig in a regular fertilizer if you would rather not bother with liquid.
Let me know what kind of climate you're in, Dawn, and I'll look for more specific info.