Use a shovel to collect and remove excessive stump grindings. Rake together a pile once few grindings remain, then shovel it out.
Turn the soil under the grindings with the shovel. Rake any grindings out of the dirt and remove them. Create a shallow hole where the stump was located.
Fill the depression with topsoil. Smooth out the soil with a rake.
Layer a starter fertilizer with a 2-1-1 N-P-K ratio over the topsoil. Moisten the soil and fertilizer prior to installing sod.
Lay the sod over the topsoil. If multiple rows are needed, stagger the seams in a brick-like pattern, centering the sod ends in one row with the middles of the sod panels in the rows around it.
Perform the finishing touches on the sod installation. Flatten out the sod with a lawn roller, then irrigate the sod with 1 inch of water, which should moisten the entire soil layer of the sod.
Continue watering the sod daily until the grass roots establish in the topsoil underneath. Add enough water daily to keep the soil layer of the sod moist.
Apply nitrogen-rich fertilizer to the sod once in the spring, once in early summer, and again in early fall. Watch the condition of the grass -- if it begins to yellow, add another fertilizer application towards the end of fall. Do not add extra fertilizer to the sod until at least 90 days have passed since its planting.
Water the sod frequently to compensate for the fertilizer. The frequency depends on location, weather conditions and the sod's grass type, but in general, water the lawn deeply whenever the grass shows signs of wilting or brittleness.