Fertilizer burn on your lawn is a big problem. The soil is essentially overdosed by a spill or to heavy an application of fertilizer. The grass turns brown and dies.The nutrients in fertilizer are typically mineral salts. Salt can have the effect of drawing moisture out of the cells of plants, both above and below ground, trying to maintain a chemical balance. When this happens the grass plants will wither and die.
If you spill fertilizer the first thing you should do is to try and get as much up as possible. As the salts will start working very quickly you must take immediate action. I would suggest that you get out the shop vac and suck up the fertilizer. After you have vacuumed the area several times I would water it heavily for the next couple of days trying to wash as much fertilizer down through the soil as possible.
If the spill is no localized in other words if your spreader setting was too high and you overdosed the lawn then you may have to take more drastic measures. You can usually determine that you overdosed the lawn if a couple of days after fertilizing the lawn turns yellow then brown. At this point the damage is done and you will probably have to reseed. Before anything else you must get rid of the excess salts in the soil. To get the salts out of the root zone of the grass plants apply powdered gypsum at the rate of 100ibs per 1000 square feet. The Gypsum binds with salt ions and helps to carry them through the soil. Then water a lot. You will need to water to the point of runoff a half dozed times or more to get the salts washed down into the soil. Once the salts are past the root zone it will be safe to repair the lawn.
You have a couple of choices when it comes to repair. You may strip the dead turf off and re-sod which is the most expensive and labor intensive. A very effective method is slit seeding. A machine runs over the lawn and place slits into the dead turf and drops seed into the slits. The slits are about one inch apart so you will need to go in two or three directions. Finally you can tear off the dead turf roto till the lawn then grade it and spread seed with a fertilizer spreader. Cover the area with a light mulch like peat moss and keep the area moist. Which ever method you use be sure to keep the area moist at all times for the 3 to 4 weeks to re-establish your lawn.