Many people will tell you that credit cards are evil, that you shouldn't use them, that you should destroy them all or lock them in a drawer. In some cases, this might be true.
If you don't have a budget that you use regularly, credit cards might be a big risk for you. If you can't keep yourself from spending money you don't have, credit cards might be a big risk for you. If you carry a balance and don't pay it in full each month, credit cards might be a big risk for you.
But if you are the type of person that has the discipline to use credit cards without getting yourself in debt, you may still have some issues getting your card to work with your budget. Credit cards can provide a lot of utility to your life, like easy spending records, fraud protection, and kickbacks like frequent flier miles or cash back.
The key to successfully using your credit card in conjunction with your budget is exactly the opposite of how you handle savings: you consider your credit card to be a part of your account. What does this mean? It means that when you charge something on your credit card, you immediately count that money as "spent" in your budget. So if you've charged $500 on your credit card by the end of the month, you should have a corresponding $500 counted against your budget categories.
In this way, you're never spending more than you should be. You're keeping to your budget. Then at the end of the month (it's best to try to align your credit card's payment date with your budgeting cycle if possible), when you make the payment to your credit card, the payment itself doesn't show up in your budget at all. As far as your budget is concerned, your credit card is just a part of your regular account.