The most common new shortcuts that you will need are:
Go to the Start Menu: Windows key (hereafter this will be abbreviated as “Win”)
Go to the Desktop: Win + D
Bring up the Charms Bar (where you can search, share, and change settings): Win + C
Bring up the App Bar (to execute commands in the current Metro application): Win + Z
Cycle through open apps: Win + Tab (with a mouse, move the mouse pointer to the lower left-hand corner of the Start Menu and then move it up)
Semantic zoom: Ctrl + “-“ to zoom out and Ctrl + “+” to zoom in (with a mouse, you can also use Ctrl + mouse scroll wheel to zoom, or click the tiny icon in the lower right-hand corner of the Start Menu)
Snap: Win + . (this will snap to the right side; you can also use Win + Shift + . to snap to the left side)
The shortcuts for the Charms are:
Search: Win + Q, or just start typing when you are on the Start Menu
Share: Win + H
Devices: Win + K
Settings: Win + I (you can change settings for the current app as well as change wireless networks, volume, brightness, turn off notifications, and shut down)
Many of the old shortcuts still exist as well, like Win + L to lock and Win + P to project to another display.
For more information, I recommend that you read this post on “Getting Around in Windows 8” from the Windows team, and download the full list of keyboard shortcuts in pdf or xps.