Command-Shift-3 has been the shortcut for Mac screenshots since 1984, and still is. It puts a file on your desktop called Picture_N containing the full screen image, where N increments for each new one you make. If you have multiple screens it will produce one image for each screen with slightly different names.
Command-Shift 4 gives you a cross-hairs cursor so that you can select an arbitrary area of the screen, and that is saved to the desktop file. Note that snapping a selection may not work if you run games in full screen mode.
Hold down Control with each of the above and the image is put on your clipboard instead of into a file. You can then paste it straight into an open document - email, image manipulation software etc. I prefer this because I don't end up with lots of unused screenshot files all over my desktop.
As Blue Monkey says, you can also use /Applications/Utilities/Grab, and there are also third party utilities like SnapzPro for more complex variations or making videos of your sceen activity.