There are many apps can do a screenshot in Android. However, I tested a few of them. They required your android phone are rooted.
Well, most of android phones have a shortcut to do a screenshot.
If you are using Samsung phone, please try to hold home key and power button for a few seconds.
For other android phone, you should try to hold volume down button (some models using volume up button) and power button for a few seconds.

These two shortcuts are the most common way to do a screen shot.