Irrigate the plants regularly and deeply to keep the soil a few inches down from the surface uniformly and consistently moist but not soaking wet. Depending on the climate, growing soil and season this may translate into watering once per week up to every couple of days during peak heat and dry spells.
Water the sunflowers at the soil line with a low flowing hose or a drip, soaker or emitter irrigation system. Refrain from watering overhead or on the stems and foliage as this increases the incidence of downy mildew and other diseases to which the species is susceptible.
Monitor the sunflower plants most carefully for signs of drought stress when young and tender and in the 20 days preceding and the 20 days following flowering as this is the most critical time for sufficient irrigation and to eliminate drought stress.