Chromebooks don't have a PrtScn key like a Windows laptop, and they don't have the Cmd+Shift+3 combo from a Mac. The shortcut is its own thing - Ctrl plus Shift plus the Show Windows key (the one above the 6 that looks like a rectangle with two lines next to it). That opens a small toolbar at the bottom of the screen, and from there you pick how much of the screen you want to grab.
The toolbar has three screenshot modes side by side: full screen, partial (drag a box around an area), and window (click any open window). One click switches between them. There's also a settings gear for audio and save-location, and a video camera icon if you'd rather record a clip than freeze a single moment.
Every screenshot lands in two places at once - a file in your Downloads folder and a copy on the clipboard, so you can paste it straight into Gmail, Docs, or a chat without opening the file. The notification that pops up after each capture has buttons for Show in folder, Edit (to crop or annotate), and Delete.
This walkthrough follows the demo from The Book of Chrome, who runs through all three modes plus the screen-recording option on an Acer Chromebook. The same toolbar works on every Chromebook running a recent version of Chrome OS.
Use a Windows laptop too? Here is how to take a screenshot on a Dell, where the Print Screen key works a little differently.