Too much fertilizer turns grass brown because it dehydrates and then kills the plant. While it is easy to remove brown grass killed by fertilizer, the key to a healthy lawn is making sure that it doesn't happen again. Fertilizer burn can happen when fertilized grass is not watered adequately, or, more often, when eager yard owners exceed recommended fertilizer amounts in an attempt to make their lawn healthier. To avoid over-fertilization, keep your lawn well watered and carefully read application rates for any commercial fertilizers that you apply.
Water the grass heavily. Fertilizer "burns" grass by dehydrating it. Before removing your brown grass spots, give it 2 or more inches of water per watering. In three weeks, some of those dehydrated brown spots may come back to life. Even if certain spots are already dead, watering the lawn thoroughly will help to wash away the fertilizer and prevent further burn.
Dig up dead brown grass along with the underlying top 2 inches of soil using a spade or small shovel..
Fill in the excavated areas with a seeding topsoil, lightly hand broadcast the seed (check the variety for application rates), rake the seed in with a trowel, lightly step on the area to improve soil contact and water thoroughly. Alternatively, skip the topsoil application, lay down a 1/4 inch of aged compost, then a section of sod cut to fit the area and then water the area thoroughly.
Water newly seeded or sodded grass patches once daily until the sod establishes itself or the grass seed is 2 inches high.