Hi there,
When we've planted a new grass area, my hubby and I have used
seeds (we use a fescue blend for our area). First we tilled the area so the ground wasn't packed down too hard and leveled it out as much as we could. Then we spread the
seed using one of those little
seed sprayers (the kind you turn the crank on the side and they fling everywhere). Then we put down peat moss over the whole area making sure to cover it well. Then turn the sprinklers on and make sure it gets plenty of water. You'll want to make sure it gets lots of water the first couple of weeks. Once it starts really sprouting you can slowly go to a normal watering schedule. Then when its all pretty tall (5-6"), give it a haircut.
That's how we've done it and its worked. Others might have better ideas so keep on checking back.