You must have a copy of the original tax return you want to update (or a transcript).
The simplest way is to prepare your correct tax return (using TurboTax for example, or other means) and print it.
Then lay the paper printouts of both returns (correct and original) side-by-side.
You now have all the information needed to prepare Form 1040X by hand.
It's pretty straight-forward.
The blank form in fillable PDF format and its instructions are available at www.irs.gov.
Mail to the same address you would mail your original tax return.
CAN I USE TURBOTAX TO AMEND IF THE RETURN WAS PREPARED SOMEWHERE ELSE?
If you did not use TurboTax to prepare your tax return, it is possible to amend the return using TurboTax but it will really be a pain. It would be better to use the software or service used to file originally. If a paid preparer made a mistake on your tax return, that tax preparer should do the amended return for you at no charge.
In order to use TurboTax to amend your return, you need to purchase the desktop software for the tax year and re-create the return EXACTLY as it appeared when it was filed with the IRS/states. Every line has to be the same. Then you have to "trick" the software into thinking you filed by saying you will mail the return. (but do not mail it) AFTER that, you use the software to prepare a Form 1040X, which has to be printed, signed and mailed to the IRS. It takes the IRS about 3-4 months to process an amended return