Hi BBBB,
I think you're on the right track -- here are a few suggestions from a fellow non-techie:
1. Turn off Time Machine -- if you have it on your launch bar, you can right click, select 'Open Time Machine Preferences', and click on the OFF/ON switch to turn it off. If it's not on your launch bar, drag it there from the Applications folder.
2. Open Disk Utility; you'll find it in Applications/ Utilities. You should not need to load an OS disk to do this. If you have both of your external drives connected, you should see them both in the left hand window. For each drive, you should see an icon for the external drive, and below it, another one for the mounted volume (if you have partitions, you'll see more than one mounted volume).
3. Select the Restore tab over the right hand window. After some introductory text, you'll see a Source window and a Destination window below it. In the lefthand window, select the volume that has your Backups.backupdb folder on the Source drive; you should see its name appear in the Source window under the Restore tab.
4. In the lefthand window, find the volume where you want the backups to be stored on your new (Destination) hard drive. Assuming you have not partitioned this hard drive, you'll only see one volume listed. Drag the volume to the Destination window under the Restore tab, and you'll see it's name appear there. You'll also see the Restore button change from inactive (greyed out) to active (black letters).
5. Click Restore, and the transfer will begin; expect it to take a long time, and for safety's sake, don't do anything else on the computer while it's going on; for 500GB I would expect it to take about 10 hours.
6. When it's finished, you should still have your Source drive intact, plus a copy of it on the Destination drive. Close the Disk Utility and use Finder to look in the Destination drive; if you see a folder that contains the Backups.backupdb folder, you should be in good shape. Unplug the Source drive, to keep it safe, and turn on Time Machine -- you will probably have to direct it to make its backups to the new drive, unless the new drive has the exact same name as the old one. When the next backup occurs, Time Machine should add it to the Backups.backupdb folder on your new drive. If not, you haven't lost anything, as long as you don't mess with the old drive!
Good luck,
Casey