If you miss a credit card payment, you will likely receive a notice from your credit card company that your account is delinquent. You should immediately make the payment and contact the company to tell them that the payment has been made. Technically, a credit card company can report a missed credit card payment to the credit bureaus immediately, but most will not report it until the account is 30 days late or more.
It is important to at least make the minimum credit card payment on time, but mistakes are bound to happen. If you realize that you have missed a payment, call the company and find out the exact amount of the payment that is now due. It may have increased due to late fees or additional interest. In addition, it is best to explain why the payment was missed; if it was the first time and it was a legitimate mistake, the company may be willing to remove any late fees and not put a notice on your credit report. If you frequently miss your scheduled credit card payment due dates, the company is not going to be as likely to want to work with you.
You should make the payment immediately; it may be done over the phone or you might want to mail in the payment. If you mail the payment, be sure to tell the credit card company that is what you are doing. Usually a credit card payment will need to be more than 30 days late before it is reported to the credit bureaus. A 30-day late payment is less damaging than a 60-day late payment, which itself is less damaging than a 90-day late payment. All of these will have a negative impact on your credit score, though.
Once a credit card payment is more than 90 days late, it will typically be sent to a collection agency. The bill collecting company will then begin sending notices and likely making phone calls to try to get you to pay. If you legitimately cannot pay, you will need to tell this to the collection agency as well as the credit card companies. Some credit card companies will settle with you, but this can be a fairly lengthy legal process. Credit card companies do have the right to sue you for unpaid balances, however, so keep that in mind before charging something you cannot pay for.