While some people prefer to use sod, it's cheaper to sow grass seeds. It might take a little longer for your lawn to grow into a carpet of green, but grass grown from seed tends to be hardier and thicker than lawns that come from sod.
Rake the area in which you want to sow your grass seeds, taking care to break up any clumps of soil and remove any rocks, twigs or other debris.
Add a layer of top soil to the entire area. Dump out in mounds, then use rake to spread. Ideally, you should have a flat, even layer about an inch thick throughout.
Add dry fertilizer with a high nitrogen content. It's best to use any pre-packaged lawn fertilizer that's available at any garden or home improvement store. You may mix in Epsom salt, one part to every 20 of fertilizer, if you want to further stimulate root growth.
Water thoroughly and let sit for a few hours.
Spread the grass seed with a mechanical spreader or by hand. Ideally, you should use about 4 pounds for every 1,000 square feet of space, or roughly 20 individual seeds per square inch.
Sprinkle top soil over the newly planted grass seeds and water again. You may want to cover with a thin scattering of straw to further retain moisture.
Water twice daily for two weeks or three weeks, ideally in the morning to minimize evaporation. Grass seed is very thirsty and needs to be kept moist at all times. Grass should sprout in two or three weeks. After sprouting you can go down to watering once a day or once every two days, depending on humidity, heat and rain. The important thing is to keep the soil moist, but not drenched in water.