The first thing you need to do is identify the type of weed you're dealing with since different weed killers work better on different types of weeds. Once you know what kind of weed it is, read the instructions on the weed killer to make sure you're using it correctly.
Many times, simply spraying a weed killer on the lawn will not be enough - you'll also need to remove the weed's root system. For this, a weeding tool (such as a garden hoe) can be helpful. Cut off as much of the weed's root system as possible, and then spray the weed killer over the top. Be sure to water your lawn well afterward so that the herbicide can reach the roots of the grass.