Mow your lawn grass down to a height of 1 inch with a mulching lawn mower. A mulching mower cuts blades into very fine pieces before ejecting it onto your lawn. Allow the grass to sit for 24 hours before bagging.
Rake grass clippings up and bag them with a lawn bag. Wait 24 hours before bagging grass clippings to keep them from heating while wet.
Rent a slit seeder from an equipment store. The slit seeder combines a vertical mower and a seed distributing machine in one device. Pour half the grass seed for your lawn into the seed hopper on the slit seeder. The seeder will distribute the seed directly into the slits cut by the vertical mower.
Start the seeder as you would start a lawn mower. Push the seeder across your lawn in a grid pattern to cut the turf and distribute the seed.
Pour the other half of your seed into the slit seeder's hopper. Make a second pass with your seeder following a grid that is 90 degrees from the first path you walked.
Water seed to encourage germination. Continue to water daily until the seed sprouts. Mow the lawn lower until the seed reaches the same height as the surrounding grass. Then raise the lawn mower decking to the normal mowing height.