Dandelions have been used medicinally and as a food source through the ages. They reseed vigorously and prolifically, produce long deep taproots and are very hard to kill. The herb is also a perennial, which means if you fail to kill that long taproot, you will see the same plant again the following year. Many companies make an herbicide formula that will rid your landscape of dandelions.
There are granular weed and feeds, systemic spot treatments and targeted sprays. Many of these bear chemical compounds which can leach into soil and infect ground water, or drift in spray and contaminate other plants and the air. A simpler solution is non-toxic warfare.
The first step is to get a thick healthy lawn, which is less penetrable to weeds and doesnt have gaps in the turf where seeds can nest and germinate. Provide good aeration and thatch when the layer of old, dead grass gets more than 1/2 inch thick. Water the grass regularly in the dry season and feed with a high nitrogen plant food in spring. When you mow keep the mower at a medium setting and let the clippings compost in naturally, to provide further food for thick growth. Good care will help prevent dandelions from getting a significant toe hold in your landscape.
Manual pulling is a chore if your yard is overrun with the weeds but it is safe and easy and even the kids can pitch in. At the very least go out morning and evening during the flowering season and pop off the heads. This will prevent them from going to seed and producing more of their kind. Next use a dandelion puller or a long handled hori hori to dig deep into the soil and get the tap root out. Caution is urged as it is easy to think you have the entire taproot but if you hear a pop that means you have left some of it behind. If you look closely at your prize you will note some of the end of the taproot is missing and that is enough to give the plant a chance at a new life.
In normal situations, pulling and preventing heads, and keeping a thick lawn are enough to keep the weeds at bay. But consider those fluffy white heads filled with air borne seeds and the neglectful gardeners or natural spaces nearby where they are free to grow to fruition and send the little parachutes out into your yard. Direct application of horticultural vinegar that is at least 20% acetic is affective. Household vinegar will not work because the acid content is not high enough. Simply spray it right on the foliage. The vinegar is non-selective so only spray directly on dandelions. It will kill the foliage, preventing the weed from intaking solar energy. This will seriously weaken and in some cases kill the dandelion, but often it will reoccur the next growing season. Citric acid works in much the same way as the vinegar and is also non-toxic.
Fight fire with fire so to speak. There are very good flame throwers to burn off the tops and foliage. They are also useful to destroy the seed head if it has already appeared. However, the chances of scorching other plants or the lawn are pretty high and you have to have a ready supply of propane on hand for instant combat. There is also a propane powered dandelion taproot destroyer on the market. It sends 180 degrees Fahrenheit through a metal spike or probe that instantly chars the taproot of the dandelion. This targeted method may effective for gardeners with few of the weeds but widespread problems require other solutions.
In large infested areas try smothering. This works best if there is no other vegetation you want to preserve. The process harnesses the heat of the sun to cook the weed down to its root. Lay thick newspaper, cardboard or black plastic over the affected area and let the sun fry the offending plants. The process if finished at the end of the growing season and as an added bonus, you have sterilized your soil.
Good care of the lawn is the most consistently effective and you will see results quickly, with added improvement year after year. Choose organic methods of feeding the lawn such as composting, using the clippings to add nitrogen, corn meal feed which is 10% nitrogen combined with regular watering, even mowing and annual aeration. The thick vigorous lawn that results will soon be impervious to all but the most tenacious dandelion and you will see a sea of green instead of a wave of yellow.