You should download a disk image file (ends in .dmg). Double-Click that to open it, it may take some time to verify. You will see a window with the Turbotax App and an icon which is an alias of your application folder. Drag the app icon into the folder or drag the app icon into your main applications folder. You can't install the .dmg file into the application folder.
You may need to be logged in as an administrator or verify with an admin password.
What step fails and exactly what does it look like? What version of the Mac OS are you using?