Primary Windows Drive Failing, Steps to Take?

I woke up this morning to a Windows message telling me my C drive was failing. I've place an order for a new hard disk, and I have backups, but I just realized that other than rebuilds where I started from scratch, I'm not exactly sure of the path to take to replicate my current primary drive to a new drive. Should I install the new hard disk into the PC, restore the backup files to it, and then reconfigure Windows to see that drive as the boot drive? Is it as simple as that, or am I missing many steps?

Since the current drive is still working, can I install the new drive, and use some other program to just mirror the failing drive to the new drive (boot records and all)? If so, is there a program that you recommend?

Depending of the drive manufacturer (of either drive) you could get a free copy of acronis (Seagates is called DiscWizard) that you can use to take a true 'image' of your current drive and put it on the new drive. Then you can remove the old drive and you should be good w/o any further work/installs.

If you want open source there is also clonezilla.

Either tool should work similarly, you'll need to boot from media, find the disk you want to image and tell it the disk to put it on.

I use Macrium Reflect to make an image for my HD about once a week or so. It's easy to use and works great. Just make sure you create a rescue cd so when you get your new one you can boot from the cd and load the image from there.