How do I paste a screenshot

As regards email, use the attachment icon (in Apple Mail a paperclip in the menu bar on new message window) to add it to your email. For the recipient, whether it appears as a inline picture or as a file attachment depends on how they have set their mail client, and you can't affect that.

As to word processors, it will will vary between various makes, but often you can just drag the image into the page, or perhaps use the Inser menu. You can usually choose between it being inline, as if it was a large text object, or floating, where text should wrap round it and you can move it independent of the text.

Note that screenshots may be very large and you may need to reduce them in size before adding them.

As noted in that article, the basic keyboard shortcuts create a file on your Desktop. Use those as you would with any other file.

If you wish to paste a screenshot, add the control key to the shortcut. It will put the screenshot on the clipboard so you can paste it.