Dandelions indicate that your grass isn’t developing healthy roots, or that there are nutrient problems in your soil. The turf may be either low in calcium, too high in potassium, or too acidic. Get a soil test to find out what’s out of whack, and use the results to strategize ways to balance out the nutrients. You can use a spray of undiluted white vinegar to kill the existing weeds (aim carefully so you don’t zap too much nearby grass), or dig out their deep root systems with a dandelion weeder.
Next spring, spread corn gluten on the lawn. Corn gluten prevents dandelions from germinating, and it also feeds the grass, making it stronger and more resistant to weeds. Use flowers as your guide; Paul Tukey, founder of SafeLawns.org, recommends applying corn gluten when forsythia blooms in the North and dogwoods bloom in the South.