To determine whether you already have administrator rights, select Start (On Windows 8, right-click on the lower right corner of your screen) and open the Control Panel.
Once you're in Control Panel, select Classic View from the dropdown in the upper-right if not already selected, and open User Accounts.
You should see all user accounts listed. If the account you are currently logged into has administrator rights, it should be listed as such under your username and/or the option Manage User Accounts will be available.
Once you have verified that you have administrator rights, make sure TurboTax is running at an administrator level. To do so, right-click the TurboTax icon on your desktop, and select Properties. Choose the compatibility tab and check the box next to Run as Administrator.
If you're having difficulties installing TurboTax and you believe it may be related to permissions, you can run the Setup.exe file at an administrator level like described for the TurboTax application above.