How to Grow Celery
The first thing you should know about celery is that its roots do not grow deep. You should make sure that the upper soil is not used up and has a good amount of organic material and nutrients. You should apply a 16/16/8 fertilizer before planting the celery, at a concentration of about half a pound per 25 sq. ft. One more very important soil preparation step is to include some bone meal or other form of calcium, as celery is very sensitive to this mineral. Soil acidity needs to be around 6.0-6.5 pH.
While celery prefers to be cool, it can't handle frosts (due to its very high water content), and it dislikes very high temperatures. So it's best to start celery seeds indoors at the end of winter, that you'll then transplant once the soil warms up and you get past the last frost. After planting the seeds, wait 2-4 weeks, until they grow about 4 leaves. Then plant them in the soil so that only the leaves showing above ground, and put them at one plant every foot.
To care for your celery, think about adding a layer of dark mulch to the surface near the plants. The dark mulch soaks in the sun's energy, heating up the soil, while at the same time offering another layer of insulation to keep the soil warm longer and preserve moisture. This is extremely important, as celery is very sensitive to frost damage, since it has a high water content. Make sure you are well past any frosts before planting.
Give your celery about 1-2 inches of water per week. Since celery is very sensitive to the water it receives, you need to stay on top of this. If it doesn't receive enough water, the consistency will be very stringy, with a strong flavor. Apply another round of fertilizer about 6-8 weeks after putting the seedlings in the ground, plus additional bonemeal or calcium supplement.
Your celery will be ready to harvest in 2-4 months, depending on the variety you planted. The base should be around 3 inches in diameter. To harvest, simply chop off the stalks right at ground level. Use the outer stalks for cooking, and the more tender, inner stalks for eating raw. Celery can keep in the refrigerator up to 2 weeks.
Growing Problems
The principal celery pests are aphids. You'll notice curled leaves, indicating aphids have been around. To treat this, apply a solution of soapy water and alcohol.
If you see white spots on your celery's leaves, this is a sign of mildew. Physically remove or clip the affected areas and keep an eye out for a resurgence. You can try not to get water on the leaves or stalk of the plant, or try to improve the air circulation so that the mildew doesn't get an opportunity to grow.
The last and most severe celery problem is the aforementioned "black heart". It's somewhat of a mystery as to what causes it, but evidence suggests low calcium is the primary factor. What happens is the ends of the stalks and leaves wilt and turn black, and quickly spread centrally towards the roots. Black heart can quickly kill the plant, with little remedy. So the most effective answer is prevention.