pests Handpick pests, such as caterpillars and weevils, during the growing season, and pluck yellowed leaves.Sunflowers are a favorite plant for introducing children to gardening because they are easily grown and require little care.Step 5 Maximize growth Maximize sunflower growth by keeping soil moist and fertilizing biweekly.Step 6 Stake sunflowers Stake sunflowers as they grow for stalk support