The installation process takes about an hour, but for the sake of your own psyche, you'll probably want to set aside a whole afternoon. Once the installation is over, you'll want to play around, organize your files, and learn the lay of the land.
Here's how you install Tiger onto a drive that doesn't have a version of Mac OS X on it already:
Insert the Mac OS X DVD (or Cd). Double-click the Install Mac OS X icon in the Cd's main window. When the Restart button appears, click it.