Growing a lawn from seed is an economical alternative to laying sod, and you also get a far greater range of options in the type of grass you can get, because most nurseries or home improvement stores carry only one or two types of sod. Lawns grown from seed also tend to be more durable because they develop a better root structure.
Pick a grass seed. Study lawn sites on the Internet (see Resources) and find a grass that is suitable to your region and your needs. Some grasses are easier to grow than others. Some types of grass are more durable than others, so if you plan to have the kids play outside on the lawn every day in the summer, pick something like Bermuda rather than Kentucky bluegrass. You also might want to consider a mixture, to ensure a year-round green lawn.
Prepare the ground. If an existing lawn was there, remove all remnants of the old dead grass. Then rake the soil and test for pH balance. You want the right mix of acid and alkaline in your soil. If your soil is too acidic, add lime; if there's too much alkaline, add ground-up bark or peat moss. Add some topsoil to the whole area as a "topper." Rake again and grade to smooth out any dips, mounds or uneven surfaces, and slightly slope away from your house.
Lightly fertilize your lawn area with a lawn starter fertilizer that is high in phosphorous. A mixture of 1-2-1 is preferred, according to the All About Lawns website.
Plant the grass seed, either by hand or by using a wheeled spreader. Your bag of grass seed should state the recommended quantity, generally in pounds per 1,000 square feet. A good rule of thumb is about 20 individual grass seeds per square inch.
Lightly rake the grass seeds into the top 1/8 inch of soil. You might want to scatter a thin later of peat moss or sawdust on top, just to make sure the seeds are in contact with the soil and are not left laying out in the open.
Lightly spray your new lawn two or three times a day, every day, for the next 3 or 4 weeks. Don't water with a strong spray; you run the risk of the water pooling and running off, carrying grass seed with it.
Let your lawn grow to a height of about 3 inches before you mow. This lets the grass stalks grow strong and also develop a solid root structure.