Restoring w/Time Machine and New Hard Drive

My 2006 MacBook's hard drive recently crashed, and I put in a new one today. I used the original CDs to install Mac OS X, and have Time Machine backups on an external drive, but have no idea how to get them onto the new hard drive. Should I have restored from the Time Machine backups during install? Is there a way to go back and do that?

Also, the laptop originally came with OS X 10.4 (Tiger), but a few years ago Apple fixed a previous hard drive issue and gave me either 10.5 or 10.6 for free, which I was running on prior to the crash. Does that complicate things?

Thanks!

The difference in os will complicate things

Your 2006 machine should run Lion at least, so I would call apple and they can sell you 10.6 or 10.7, they dont advertise it on the online store but give them a call and see if they can sell and ship you at least a Snow leopard disk

then you can do a fresh install, the first thing the install will ask you on completion is whether you have a connected time machine drive to restore to

Thanks! I'll give that a shot.

A follow-up in case anyone's interested:

I borrowed an OS X 10.6 (Snow Leopard) disk from a Macbook Pro, and started the install. After the laptop restart step, it wouldn't let me continue with installation, since I wasn't running 10.5, but it did have a button for restoring from time machine.

Plugged in my external, let it restore, and everything's fixed!