This is reported in Box 4 of your Form 1099-R as federal tax withholding. The default withholding rate for an early withdrawal from a retirement fund is 20%. This will be added to your other withholding to be considered a payment towards your taxes.
Your tax return will calculate your actual tax liability on the withdrawal which will include income taxes and a 10% early withdrawal penalty. Your withholding that was already taken out will then be applied against these amounts to determine your refund or additional balance due.
The tax return serves as a reconciliation of income and withholding to figure your actual withholding. For example, if you are in the 15% tax bracket and you owe the 10% penalty, this is 25%. If you only had 20% withheld, you would owe an additional 5%. If you are in the 10% tax bracket, then the exact right amount was withheld and they would essentially cancel each other out.
The withholding was a pre-payment of your taxes and the tax return actually calculates the tax. You are not paying the penalty again. Just make sure that the amount originally taken out is in Box 4 of Form 1099-R and make sure you entered it when inputting your form.
Note: All income, taxes and withholding are accounted for together to determine your end result.
