The tag below your question says you are using TurboTax Online. If that is correct, your tax returns are not on your computer. They are on the TurboTax server. You can sign in to your TurboTax Online account from any computer and all of your information will be there. You do not have to move anything.
If you are using the desktop TurboTax software, please clarify what exactly you want to move, or what you are trying to do. Do you want to move your tax return data files, or do you want to move the TurboTax software? If you want to move your tax return data files, see the article at the link that xmasbaby0 posted above.
You cannot move the TurboTax software from one computer to another. If you want to have the TurboTax software on your new computer you have to install it on the new computer from the download (or from the CD if you have a CD), the same way that you installed it on the old computer.
