If a child is born to an unmarried couple and there is no set custody, how is child support determined?

The fact that the parents are unmarried doesn't affect the amount of support. If there is a dispute about paternity, dna tests can be ordered.

Support is determined based on a formula, primarily determined by the  incomess of the two parties. Custody isn't a factor, unless there is shared custody with the paying parent having the child for 40% or more of the time, which could result in a reduction in the support obligation.