How to have a healthy lawn without chemicals

Healthy lawns naturally resist pests and disease
Crowd out weeds and reduce post damage by promoting a healthy, vigorous lawn through proper fertilization, irrigation, and mowing. Improve thin areas with aeration and overseeding. A healthy turf will need far fewer pesticides.

Accept a few "weeds" in your lawn
Some, like clover, may look fine. Target the problem weeds, leave the others.

Pull, don't spray
Remove problem weeds by hand in the spring and fall. Don't cover your entire lawn with 'Weed & Feed' just to kill a few dandelions. Pincer-type long handled weed pullers are available at many garden stores. They work well in moist soil, with no stooping. Pull dandelions when they're young (for best results get as much root as possible).

However, most so-called weeds like dandelions are beneficial and beautiful.  For example most of the dandelion plant is edible.  The leaves are great is salads and the flowers atttract bees.