It took about two hours, but Time Machine restored the system perfectly while I worked on another computer. I'm guessing that Time Machine saved me a couple of days of reinstalling a new System and all the applications that were on the Mac. Just knowing that Time Machine is at work removes a lot of anxiety. If I'm working on an important document and it crashes, I know that Time Machine checks regularly and makes a new backup when a file has changed. I can always go back in time, select a backed up version of the file, then click "Restore."
To use Time Machine, you'll need to connect an external FireWire hard disk to your Mac that serves as a backup volume. Or you can buy Apple's wireless backup device called Time Capsule. Same thing, only wireless. And with Time Capsule, you can use it as the backup volume for multiple computers.
Once you connect a dedicated hard disk (or Time Capsule) and set it as the Time Machine backup volume, backups are automatically performed in the background whenever a file is created or modified.
To restore an item (a file or folder), select it, then click the Time Machine icon in the Dock (below).
The screen transforms into a star field (below) with windows receding into the background (back in time). Click the 3D arrows to transport back in time to the last saved version of the selected file. Or hover your cursor over the vertical timeline on the right side of the screen to select a backup date. When you find a version of the item you want to restore, click "Restore" in the bottom-right corner. The file is restored to your Mac and its current environment. Oh so easy. And convenient.
To restore an entire System, as mentioned above, it's a little more involved because you have to start (and run) your computer from another System, such as from your original install disc, or from a connected bootable backup disk.
I only mention this because I know soooo many people who don't back up regularly. In fact, the only ones I know who back up regularly are a tiny handful of wise, stress-free, souls who use Time Machine. When it's this easy, go ahead and do it dangit.