To make a screenshot of your current screen state you don't need any extra software under Android 4.0 or newer. Simply press and hold both Power button and Volume Down button in the same time. On some devices it may be necessary to press Power and Volume Up button instead.
A slick animation appears showing you that screenshot was taken. Additional information about writing screenshot will appear next on your status bar.
All your screenshots will be written in PNG format and stored in
Pictures/Screenshots folder (at least on Samsung Galaxy Nexus), with a name matching pattern
Notice: To take a screenshot, you must press both button in the same time, not one after another. If you have some problems with that, try to press Power button first and then immediately after press Volume Down button. In this combination, it is easier to get the effect, because generally Power button reacts with some delay, while pressing Volume Down button gives immediate result.
Also note, that when you're device is connected to a computer, its SD Card is locked and not accessible. Making screenshots is possible, but all of them will be written in some temporal folder and not transferred to
Pictures/Screenshots folder until you disconnect your device from your computer.
On some devices it may be necessary to press Power and Volume Up button instead.