Depending on the location of the weed, you can often kill it with boiling water. Just pour over the weed and it will often die back. You can also use vinegar in the same way, which works for more stubborn weeds. Don't try this in your vegetable or flower garden, though. It works best for killing weeds in sidewalk cracks and between bricks. Otherwise, the only solution is as relache says: pull up the entire plant. For things like dandelions, you'll have to keep digging and rooting.