First your must go to the court where your case is and get the required paperwork. The court will tell you what type of form. Probably a motion for a temporary order or a complaint for modification. This is for both a divorce and paternity.
Step2
Child support is base on the parties weekly gross income, age of the child, who pays/provides health insurance and daycare expense.
The easiest way to get more support is if your child becomes a teenager. There is usually a 10 % increase just for this. Another way is if you are the custodial parent and you decrease your income and become unemployed.. If you work for cash you can also get more support because this is not racked/taxed, but same goes for other party...
Step3
If the parent paying gets a better job or promotion that is a way to get an increase...
You can also try to get money for a clothes allowance or extracurricular activities..
Authority 
