Typically when it comes to taking a screenshot, a series of keys is used to trigger the action. For Android devices (running 4.0 and above), the standard key combo is pressing the volume-down and power buttons at the same time. For iOS it's a combination of the home and power buttons. Chromebooks, and really ChromeOS in general, have their own set of keyboard shortcuts to initiate a screenshot.
To take a standard screenshot of the entire screen, press the Control (Ctrl) key along with the switch window key at the same time. The "switch window key" is has an outline of multiple windows on it, sitting just above the row of numbers; placement may vary depending on device.
A few seconds after using the key combo you'll see a notification informing you that the screenshot was successfully captured. To limit the screenshot to a section of the screen, just add the Shift key to combination (making it Control - Shift - Switch Windows key). The mouse pointer will turn into a crosshair, allowing you to select the area you want saved for all eternity.
Accessing your screenshots can be done one of two ways. You can either click on the notification, or you can open the app launcher and find the icon labeled "Files." Your screenshots can be found in the Downloads folder. From there you can upload the file to Google Drive, share it via e-mail, or do whatever it is you do with screenshots.
For more Chromebook how-to content, be sure to check out this page dedicated to all things Chrome OS.