Brown spots or patches in a lawn can result from several causes. The vast majority of all brown patches are caused one of five common causes:
It is important to note that a small brown patch is not the same thing an area of lawn that is brown. Large areas of dead lawn can have a variety of causes quite different from those that cause small brown patches.
Fertilizer burn results when too much fertilizer is applied to one spot. The nitrogen in the fertilizer will kill the grass if too much is applied. Even distribution is key when using chemical fertilizer. Alternatively, liquid or organic fertilizer will reduce the incidence of nitrogen burn.
As to repairing the damage, repeated soaking of the affected area will wash away the excess nitrogen. Depending upon the drainage you may be able to reseed the spot in a few days to a few weeks.
When grass roots are constantly exposed to water they tend to rot. When the roots rot, the grass dies and turns brown. This often occurs in low spots in a lawn. Water pools in the low spots every time you water or when it rains and the roots remain saturated. It can also result from improperly arrayed sprinklers where overlapping spray patterns cause severe over-watering. Also, soil compression can result in poor drainage which when combined with any of the other causes, makes the problem worse.
The key here is to ensure that the lawn has no low spots in which water can pool and that the lawn has good drainage. Dig out lows spots, are refill them to the proper level with get soil and then reseed the area.