Work the soil with a tiller to break it up as fine as possible. Make the passes with the tiller across the side of the hill rather than up and down the slope. Rake the soil smooth in the same direction across the hill. The horizontal lines in the soil from the rake or tiller action will slow the flow of water.
Broadcast the seeds on the hillside. Use a mixture of perennial and annual grasses. The perennial grasses, which grow year after year, become the permanent lawn while the annual grasses grow quickly and create the root network that will hold the grass in place on the hillside.
Rake the soil to cover the seeds with about a 1/2 inch of top soil. Cover the hillside with open mesh burlap, available from home improvement stores, or straw. Drive stakes through the burlap and into the soil to hold it in place. Spread the straw bales at the rate two bales per 1,000 sq. ft.
Water the seeds whenever the topsoil feels dry. Use a soaker hose to supply the water gently to the hillside. Provide enough water to soak the soil to a depth of about 5 inches but turn it off before puddles form on the surface.
Monitor the grass as it starts to germinate and sprout. Remove the burlap when the grass sprouts are about 1/2-inch long. Continue the watering schedule as the grass grows. Mow the grass when the tallest grass blades reach about 2 inches tall.