Even the best cared for lawns will have an occasional dandelion. They are difficult to completely eliminate, and the entire plant (root and all) of the dandelion needs to be removed or they can grow right back. To rid your lawn of dandelions, use a product such as Ortho® Weed-B-Gon MAX® Weed Killer For Lawns. Apply it to the dandelions to kill them without harming the lawn.
The best way to attack dandelions is to kill the whole plant, taproot and all, and then keep new weeds from establishing themselves in your lawn. To take care of your dandelions, apply Scotts® Turf Builder® With Plus 2® Weed Control in the spring. If that doesn't get them, follow up in 2-4 weeks with an application of Ortho® Weed-B-Gon MAX® Weed Killer for Lawns. Just be sure to follow the instructions on the label.
Don't hand pull them, as they will grow right back unless the tap root (often 2-3 feet deep) is completely removed.
A thick lawn is the best method for preventing dandelions and other broadleaf weeds in the lawn. Mow your lawn at a high setting on your mower, and follow a regular feeding program to achieve a lawn that is thick enough to keep weeds like dandelions from establishing in the first place.