Planting up in early spring will help ensure the best flavor, and making sure your Tarragon doesn't get too much direct sun in hot climates is best. You'll also need to select a sandy, well-draining soil.
How much you water your Tarragon will depend on the weather conditions and the maturity of the plant.
Young Tarragon will benefit from watering on alternate days if you're experiencing prolonged hot, dry spells. Mature Tarragon, however, should be fine with a light watering every few days.
Tarragon doesn't need fertilizer to do well. The best flavor is achieved when it's planted in low-nutrient soil. If you're going to use some, an all-purpose variety should only be applied in the initial planting stage.