The new hard drive is internal. My question is after I install the drive how do I install mountain Lion so I can than do a restore from Time Machine.
Another way is to simply clone your current startup drive to the new drive. Make sure the new drive's partition map is GUID. You do this in Disk Utility when you partition, or repartition the drive. You can also check a drive's map in Disk Utility. Launch the app and highlight the 2 TB drive's physical drive icon. Like below:
Then look at the lower right of DU's window. If the drive is already GUID, it will say so, as per the next example:
Once the new drive is setup correctly and ready to use, you can clone your current startup drive to the new one using Disk Utility, or one of two excellent cloning utilities; Carbon Copy Cloner, or SuperDuper!. This will save you the trouble of installing OS X and incorporating your Time Machine backup to finish. It will already be done as the new drive will be an exact duplicate of your current startup disk.