A screen shot doesn't actually post to the clipboard, it saves in your gallery under Screenshots. However, you should see it in the notification bar. From there you can just select "Share Via" and load it into whatever you want to use to send it somewhere.

When I slide my palm left to right on a screen, I capture the screen into the clipboard.

How do I paste from it into a document?

I notice I can see the clipboard by holding a long press on the microphone in the keyboard. However, I notice the picture previously captured does not show there.

Should I use Gallery in some way to recover that picture?