If the debt on a credit card is D and simple interest at rate s% per annum applies, then after a period T measured in years the interest will accrue: DTs/100 and the credit card company will expect a minimum monthly payment m (due by a certain date) based on the total debt plus interest: m=(D+DTs/100)/12. The credit card user can pay more than the minimum monthly payment in order to pay the debt off faster. On the next month, the credit card company will note the balance owing, according to the amount the user has paid, and will recalculate the new debt plus interest and provide a new minimum monthly payment, based on a rolling year, i.e., for another period of 12 months from that date. If the user defaults on payment or pays late, there will usually be a penalty which the company will add to the user's debt. So the debt is changing month by month according to how much the user is paying and whether the user defaults or pays late. Penalties will accrue interest, too, because they're added to the user's debt. If the user pays exactly the minimum payment each month and doesn't purchase anything with the credit card, the debt will be paid off in one year.
The process is similar when compound interest applies, but the calculations will be different. Interest will usually be compounded monthly, but the minimum monthly payment will be higher because it's based on the annual compound interest rate c%, which is c/12% per month. If the debt is D then the minimum monthly payment is D((1+c/1200)^12)/12. If the user pays only the minmum payment, the debt will be paid off in the year, but the total amount will be higher than if simple interest had been applied.