How many points will your credit score go up when you pay a minimum amount due off a credit card?

It depends on other factors, you should pay the credit card ontime.
keep in mind that you must reduce the balance of your credit cards to 30% and below of your credit limit. If you have a credit card with a $5,000 limit, your balance reported to the credit bureau should be $1500 and under in order to have a excellent credit score. If you go over this amount it will affect what is called your "utilization rate."
Credit score formulas respond favorable to utilization 30% and below. It's a good idea to assess all of your credit cards and align them correctly with this formula. Source Credit Bible by Phil Turner.