The next step depends on what you call Backed Up.

If your backup was done with Time Machine, then have the external drive connected to the Mac while you install
When you get to the question about having data to transfer from Another Mac or a Time Machine backup or anywhere else, choose Time Machine.
From that point on, just follow the instructions.

If your backup was just you copying files from the internal to the external, the procedure is different.
Once OS X is up and running on the internal, connect the external drive and just drag and drop the CONTENTS of your backed up folders into the corresponding folders on the internal.

For example: If you copied the entire Documents folder from internal to external, find the Documents folder on the new external and open it. Now open the Documents folder on the external and drag the contents from one to the other. Do NOT drag the entire folder, just the contents.
You should be able to just replace the iTunes folder and the iPhoto folder by, in this case, dragging the whole folder onto the internal.

If your Backup was done with 3rd party software, the install OS X, and the 3rd party software and follow their instructions on how to restore

Hope that lot helps some