The most-common reason for yellow spots on a lawn is a lack of nitrogen in the soil. This causes the grass to first turn a very pale yellow, which then deepens to a bright yellow. In order to fix this, a nitrogen-rich fertilizer must be applied to the grass. It's best to do this for the entire lawn, since, generally speaking, if one spot is affected, all of the lawn is susceptible.
Other causes for yellow grass are diseases and pests such as grubs. In these cases, the grass will typically turn slightly yellow in big patches before turning brown. When this is spotted, it's necessary to dig up the spots that are affected before the problem spreads to the rest of the yard. The dead grass and accompanying dirt should be disposed of in plastic bags or burned to keep the diseases and pests from spreading.
Thatch is a common occurrence in yards, particularly when lawn clippings aren't bagged. Clippings, leaves and other organic materials build up on the lawn and create a thick mesh at the level of the soil. This prevents new grass from growing properly and keeps existing grass from getting the nutrients it needs. Over time, this will create patches of brown, dead grass. To prevent thatch, a yard should be regularly raked in the fall, and clippings should be bagged.
If a lawn already has a thatch problem, it will need to be dealt with to keep the grass from dying. A dethatcher can be rented from a local hardware store, or if the problem is recurrent, you may want to consider purchasing one. Run the dethatcher across the entire lawn at least twice a year, once in spring and once in fall. This will make the lawn look torn up, but it will rebound quickly.