Help with hard drive failure restoration from Ext. Hard Drive

I have a WD My Book Essential 2 TB external hard drive.  It has been set for continuous backup on my Vista operating machine (I will call this the Vista PC).  I recently purchased a new PC running Windows 7.  I had moved many of the files from my older Vista PC to the new PC when the hard drive on the Vista PC failed.

I would like to plug the WD external hard drive into the new PC and manually transfer the remainder of my files to the new PC.  After that is complete, I would like to set up the WD external hard drive to automatically backup the new PC. 

Can you please advice how I should do this.

Do I just plug the USB cable into the new PC?  Will it just load the driver and then be available?  I was concerned it might be confused thinking it was still connected to the Vista PC or perhaps want to start backing up the new PC immediately. 

Your advice would be greatly appreciated.

Hello, you can go ahead and just connect the external hard drive to the new computer, if you a re using smartware to do the backup, it will just create a new backup.