Copy and paste
Select one or more items and press Ctrl/Cmd + C to copy them, then Ctrl/Cmd + V to paste. Pasted items land slightly offset from their originals, already selected, so you can immediately drag them into place.
Ctrl/Cmd + X cuts (copies, then removes), and Ctrl/Cmd + D duplicates the selection in place without touching what's on the clipboard.
Between boards
Copy and paste works across two different boards, not just within one — copy items on one board, switch to (or open) a different board, and paste there. The clipboard is kept in this browser's own local storage rather than only in memory, so it survives switching boards or even closing and reopening the tab, until you copy something else.
Pasting images from outside the app
Ctrl/Cmd + V also accepts an image copied from somewhere else entirely — another application, or an image copied from a web page (Copy image or Copy image address) — and adds it to the board as a new photo, the same as using File → Add photos….
Which one gets pasted? Whatever you copied last: items copied on a board, or an image (or image address) you copied somewhere else after that. Edit → Paste in the menu always pastes board items.