Help. I can't figure out how to update software and migrate Time Machine after installing a new harddrive?

Yesterday I upgraded my harddrive from 80GB to 500 GB. I carefully saved everything on my external harddrive via Time Machine but it's not letting me migrate it. I had recently installed Mountain Lion but it was a download. The latest actual OS disc I have is OS X - Leopard. I just can't figure out how to get the updates so I can finally migrate my Time Machine backup. Does this make sense? Thanks in advance!