There are two varieties of tarragon - French and Russian. Grow the French variety if it is your intention to consume it. However, tarragon grows better in cool climates, and often attracts a fungus in humid climates which kills it.
Purchase as a seedling. French tarragon doesn't set seeds and is propagated by cuttings. Russian tarragon can be purchased as seeds. Plant in spring or summer.
This plant will die back in winter but regrow each spring. Ensure that you have marked it's location so that you do not damage the dormant roots in the cooler months. Cut the stems back to about 3 inches. It is considered a frost sensitive plant, but the frost will kill the leaves and not the plant, allowing it to grow back in spring. However, it is late to reappear in spring so do not lose hope too early that it has died.
Ensure it has well draining soil, a neutral pH and at least part shade.
Every 2 years, dig up the plant and divide it. This plant can strangle itself with it's own roots and requires them to be divided or spread out before being replanted.
Tarragon grows very well in a post, and this allows it to be moved around your garden to companion plant.
This is not a crop that needs to be succession planted. One plant is generally sufficient for a family.
Harvest the leaves as needed. It can be dried and stored for winter. It can also be soaked in vinegar to flavour salad dressings.
It grows well with sage, rosemary, parsnip and thyme.
Tarragon is a light feeder. A drink of fish fertiliser once or twice during spring and summer is sufficient.