Most cool-season sods are improved Kentucky bluegrass varieties because their spreading rhizomes intertwine to form a strong sod. Use high-phosphate starter fertilizer when laying sod, just as you would with reseeding. Keep sod in shade so it doesn't dry out and lay it in a staggered brick-like fashion, matching the edges closely to prevent the sod from drying out. Seed at the right rate. The larger the seed, the higher the seeding rate.
Studies show that there is no benefit from seeding more than the recommended rate.
Excessive seeding rates create too much competition between the seedlings. Seeding at the correct rate or slightly lower encourages tillering - lateral spreading of the grass plants. Then apply the seed in two different directions at right angles to each other. This assures more uniform coverage. If you are reseeding a small patch, you can mix 1 part seed to 3 parts soil in a bucket and then evenly spread the mix over the patch.