Call and Beg.
As soon as you get a representative of that company on the phone, apologize like you've never apologized before. Don't panic, stay calm, but make it clear to whoever you get through to that you're very sorry, and things like this never happen to you. During this, be honest. If you forgot to pay, tell them, and if you didn't have the money, say that too. 

Usually, these credit card companies are lenient, as the sensible ones want to keep you paying interest to them for a long time to come, so its not really in their interest to punish you. Remember to be very grateful when they let you off, and tell them it won't happen again. Also, during this conversation, never become angry or frustrated, as you are the one that broke the terms of the contract. 

However, if these companies don't seem to want to budge be willing to transfer your balance elsewhere as a punishment for them if they won't let you off this one mistake. Transferring your entire balance to another card will make them sit up, take notice, and start making you much better offers than you ever got before.

Plead For This Not to be Put on Your Credit Report. 
Do everything you can to persuade the company not to add your late payment to your credit report, at least if you want to apply for any credit in the next few years. Remember that any late payment could be a black mark against your name for as long as ten years.

If, however, you fail, don't worry about it too much. As long as there's only one late payment, it isn't life or death, especially once a year or so has gone by. It's the people who consistently pay late who get the truly terrible credit ratings.

Use This as a Lesson and Mail Early.
This advice may be obvious for the people whose payments didn't make it in time, but its good advice for everyone, as it saves you from trying to find money at the last minute. It is just poor practice to wait until the day before the deadline to make your credit card payment, as there are just too many things that can go wrong. In a more general view, also never let your bills stack up on you, as letting them sit only increases the possibility that they don't get paid.

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