Answer: If you re-sod, you'll have instant results; if you re-seed, it will take a few weeks, but eventually the spots will fill in. I'd start by digging out the dead grass (roots and all), then roughing up the soil. You can purchase strips of sod at nurseries and home improvement centers. Cut the sod to size and place it firmly on the prepared area. It's important to have good soil/root contact. Water well and water often to make sure the roots grow down into the soil.
Seeding will take roughly the same steps; rough up the soil and broadcast seeds over the top; rake them in lightly then cover with a thin layer of peat moss to keep the area moist. Water frequently so the seed bed never dries out. In 7-10 days the seeds will sprout and you'll see a slight green tinge to the area. Water frequently and mow when the blades are 3" tall. The area will fill in as the grass matures.
Either way, you'll have a lush lawn in a short time. Enjoy!
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