First off, let me not assume everyone knows how to create a screenshot on their phone. Typically it requires holding a home button and either the volume down or sleep/wake button on the side of the phone.
Once you know how to take a screenshot, they inevitably start accumulating in your photo library. That leads to periodically combing back through the last several months to delete these or admitting screenshot bankruptcy (a.k.a. ignore them).
Great news, though! There are several quick and simple apps out there who can clean up your library with one quick search. My favorite of the bunch is Sharkie.
Scans when you launch it, presents you with visual of all it finds, and then you click and delete. Dead simple.