It depends on the type of mistake you made:

Many mathematical errors are caught during the processing of the tax return and corrected by the IRS, so you may not need to correct these mistakes.
If you didn’t claim the correct filing status or you need to change your income, deductions, or credits, you should file an amended or corrected return using Form 1040X, Amended U.S. Individual Income Tax Return.
When filing an amended or corrected return:

Include copies of any forms and/or schedules that you’re changing or didn’t include with your original return. To avoid delays, file Form 1040X only after you’ve filed your original return. Generally, for a credit or refund, you must file Form 1040X within 3 years after the date you timely filed your original return or within 2 years after the date, you paid the tax, whichever is later.
Allow the IRS up to 16 weeks to process the amended return.