Copy & Paste works like this:
tap any word you want to copy and it will be highlighted. There'll be two visible lines with a circle on the bottom appearing on the left and right of the marked word. These lines can be tapped, held and moved, in case you want to expand you selection.
On top of said selection a circular button will appear, allowing you to copy your selection to the clipboard. If you now want to remove the selected text (which would make it cut rather than only copy), just tap the back (delete) button on the keyboard.
The recently copied text can be pasted by tapping the circular icon on the top left of the keyboard.