Till the old grass down to a depth of 4 to 6 inches. Remove as much of the debris as you can, including the roots of the old grass. Sod must be in contact with soil to take root, so loosening the old grass will create a better base.
Spread a starter fertilizer with a nitrogen-phosphorus-potassium ratio of 2-1-1. Water the area until the soil is moist to help the food get into the soil.
Load sod into a wheelbarrow and take it to the planting area. Gently lift out the sod piece by piece, being careful not to tear it.
Take out a full strip of sod and lay it down along the outer border of the lawn. Put other full strips as close as possible to the first one to eliminate gaps and lines.
Work your way across the lawn, laying down as many full strips of sod as possible. Focus on pulling them tightly together without ripping them.
Fit irregular spaces with smaller sod pieces cut with a sharp blade. In corners, overlap the sod over the border and go back later to cut off the excess. If you need to use small pieces of sod, make sure they are in the middle of the lawn. Small pieces on the edges of your lawn tend to die.
Run a half full roller over the sod. Water until the top 6 to 8 inches are moist.