The menu button of the onscreen keyboard (lowest button on the left side of the keyboard) has cut, copy, and paste.
If you're using a hardware keyboard, you could also use the shortcuts Ctrl-X, Ctrl-C, and Ctrl-V.
Some programs like the webbrowser or XTerm also have such items in their Edit menu.

Although difficult, it's possible to select text for copying in the browser by double clicking and then dragging.