Dandelions love to grow in compacted soil with full sun. The best way to control them without chemicals is to aerate the lawn and fertilize with a fall and winter lawn food this fall. Then in the spring the new grass can wake up and grow faster than the dandelions and crowd them out. This will take several years, however. You can also dig them out with a knife or a stand-up weeder that pulls the roots out. One trade name is "Grandpa's dandelion weeder" but there are other versions sold at big box stores. Add lime to your lawn as too much clay can cause compacted soil, and lime helps to break up clay soil. If you do want to resort to chemicals, you can use a broad leaf weed killer on the lawn that you hand spray just on the dandelions not on the entire lawn. Dandelions are edible and nutritious but do not eat any weed unless you know it has not been treated with an herbicide.  Go slow, don't expect a quick change but over time; after improving the soil and thickening the lawn, your crop of dandelions will turn into a pretty good lawn. Keep growing, Marianne Binetti