Taking a screenshot has always been relatively easy in iOS. You simply hold the power button and Home button at the same time.
It used to save the screenshot in Photos, but now, it puts a thumbnail on the screen. If you click the thumbnail, you’re taken into a new editing screen, where you can make multiple edits: crop, add arrows/lines/shapes, put in text, sign it, magnify a section, highlight, write on it, type on it (and change the font), select sections, undo/redo your actions, or use the lasso tool to grab your annotations and move them (even scribbles and highlights). Too many!
When you click Done, save the screenshot to Photos, or just delete it, if it was for fun. (This is in addition to the tools you get in Photos for cropping, rotating, filtering, and adjusting color and contrast.)