They determine it by how much you make, how much you spend on your own necessary expenses (housing, food, base necessities), and how much you would need to spend on 50% of the care of the children.
The court will look at the non-custodial parents income and then look at how many children there are. From there he/she will figure out how much this person will pay. Then the judge will look at how much expenses are and usually divide them in half.
Most of the time child support is determined by the amount of income the responsible party has. Each state is different when determining the percentage of income that is used.
