On Mac
Use Command + Shift + 3. The screenshot usually shows up on your Desktop, with a name like “Screen Shot 2015-02-14 at 9.29.31 AM.” You can edit the image (crop it, etc.) if you like.
You can also use Grab, which will let you select a specific portion of the screen (rather than the whole page). If you have Mac OS X v10.4 or newer, find Grab under the File menu in Preview now has a Grab submenu in the File menu. Otherwise, look for Grab in the Applications folder and then in the Utilities folder.
On Windows
On Windows 8, use Windows Key + Print Screen. On Windows 7, use Print Screen and then paste the image into an image editor.
You can also use the Snippings Tool (also on Windows 7), which will let you select a specific portion of the screen (rather than the whole page).
Additional Tools
For more sophisticated screenshots as well as screen capture videos, you can try Jing, which is free for both Mac and Windows, or Skitch, which is free for Mac, Windows, and iPhone.