We're only human after all. Given that, and the fact that filing income tax forms can be complicated stuff, there is a risk of making an honest mistake.
So, what do you do if you've filed a federal return and realize after the fact that you made a mistake?
If it is a simple math error, chances are that it will be caught and corrected by the IRS as the return is processed.
If you didn't report all of your income or failed to claim a tax credit that you are due, then you should file an amended return, using Form 1040X.
Submit it after you get your refund, or by the time the return is due, whichever comes first.
If you need to file an amended return, do it within three years after the date you filed the original, or within two years after the date you paid the tax, whichever is later.
A return filed early is considered filed on its due date.