Cut out the dead areas of sod using a utility knife, removing it until all of the brown is gone and only green grass remains around perimeter of the area.
Fill the hole with 1 inch of top soil just until it is at the surface of the surrounding soil. Since the sod is new, you will not need to do any soil amendments, which was done at the time of the initial sod installation.
Spread the grass seed on top of the soil using the amount specified on the seed packaging. Cover the seeds with a 1/4-inch layer of peat moss until the seeds are no longer visible.
Step lightly on the repaired area to firm it, but do not stomp down on the soil.
Water the soil to a 1/2-inch depth using a garden hose with a sprayer attachment. Afterward, water the repaired areas at least twice per day to prevent them from drying out until the seeds germinate. After germination, switch to the same watering schedule you use for the remaining sod.