Update, November 16, 2012: The method for pinning Web sites with Chrome was added to this blog post.
The Windows 8 Start screen comes prepopulated with lots of tiles, some of which you won't ever use. Instead of wasting that precious space, you can remove the tiles you don't use and pin your favorite Web sites to the Start screen for quick and easy access. Here's how:
Step 1: Open Internet Explorer from the Start screen and go to the Web site you want to pin.
Step 2: Click the pin icon in the lower right-hand corner of the address bar, then select Pin to Start.
Step 3: Change the description to something shorter, so it's not cut off at the end of the tile, then click the Pin to Start button.
If your primary browser isn't Internet Explorer, you can also pin sites using Chrome, though, the tiles won't look as nice. Go to Settings > Tools > Create application shortcuts. Create a desktop shortcut, then right-click on it and select Pin to Start. A drawback to using Chrome to pin sites is that they're application shortcuts. This means that you won't be able to access any of Chrome's settings, bookmarks, or the toolbar when you launch the tile this way. Unfortunately, there's no way to pin sites with Firefox at the moment.
That's it. By default, new tiles will be added to the far right side of the Start screen. If you want to move it, just click on the tile and drag it over to your preferred location.