If you can water the area where a dog has urinated within 8 hours, that will help prevent a lot of the burned spots. When I say water, I mean water well! Unfortunately, if it isn't your dog, you may not be aware of the spots until the damage appears.

When the spots are mild, the lawn will generally repair itself. You can try patching with sods if the damage is bad or you could reseed. To reseed, just scratch the dead spot hard first, spread seed that matches your lawn, press down so that the seed comes in contact with the soil, water and keep moist until germination.