Overwrote Mac when installing Windows

You can try booting up your Mac through Internet Recovery to try to restore your backup. To do so, hold down Command, Alt and R keys while your Mac is starting up. Your Mac may ask you to connect to a Wi-Fi network.

After booting up, plug the external drive with the backup, choose the option to restore a Time Machine backup and follow the steps. I suppose you made the backup with Time Machine; if you made a clone of your OS X drive, you have to follow different steps.

In that case, how did you make the backup? Did you just copy the files you wanted to on the external drive or did you use an app to make backups? Time Machine comes with the Mac and it is the most used backup utility.

If you do not know if you were using Time Machine to make backups, try the steps of my first reply. It will let you restore the backup if you used Time Machine.

However, if it did not work and you did not make a clone of your hard drive, you'll have to erase everything from your hard drive and reinstall OS X.

1. Follow the steps on my first reply to boot up through Internet Recovery, and open Disk Utility.
2. Your hard drive should be highlighted in blue at the top of the sidebar (if it is not, press it). Then, go to the "Erase" tab and erase the whole hard drive.
3. Close Disk Utility and reinstall OS X.
4. After reinstalling OS X, you will be able to restore manually the files you backed up.

In step 2 you may not see the "Erase" tab (Disk Utility was completely redesigned recently), but you will see a "Erase" button at the top of the window. It does the same job.