Turfgrass can be established a variety of ways.
The method you choose will be determined by the situation your lawn is in. Do you have a new construction? An existing lawn that is thin and rough? A fair lawn that is just a little thin? Depending on what condition your lawn is in will determine where to start. Let's say you have a lawn that is in fair condition but needs thickened up.
An easy way to do this is to Aerate and overseed. An aerator is a machine that will poke a hole in the ground (thousands of them actually) and remove a core of soil and leave it laying on the surface. These are called core aerators.
Some aerators will simply push a spike into the ground creating a hole, this type is not as good. To start with, mow your grass as low as you can safely, don't throw rocks and dig dirt with the mower, but get it down to about 1" high.