Clear the weed covered area using a weed eater and shovel. Cut the weeds off at the base and then rake them up into piles.
Till up the soil with a rototiller. The roots of the weeds will turn up on the surface of the soil, killing them. Rake up all the roots and dispose of them.
Level the newly tilled area with a shovel and rake. Fill low spots using a shovel with dirt from the high spots. Smooth out the area using the back side of the rake in a back and forth motion.
Measure the square footage of the area you wish to seed using a tape measure to determine how much grass seed you'll need.
Spread the seed pver the tilled area using a hand-held or wheel-based grass-seed spreader. Cover the area with a thin layer of moisture-absorbent material such as peat moss or straw to hold in moisture.
Water the area with misting sprinklers positioned to spray the mist into the air to avoid moving the grass seed two to three times daily until the grass is two inches tall.