Most browsers do not allow javascript to access the system clipboard directly, which makes it difficult to copy/paste text in/out from the operating system to X windows in your browser VNC window. So we have to jump through a couple of hoops to make it work:
Copy: Simply highlight a region in one of your VNC X windows and then click on the Copy To System Clipboard button at the top. The region will be copied to your system clipboard, you can then paste it with your operating system paste key or menu item.
Paste: To paste from outside the VNC window, into one of your VNC X windows, you have to do it indirectly by first pasting into the paste box at the top left of the window, and then using the X paste key (or mouse button) to paste into one of the VNC X windows.
Copy paste between VNC X windows behaves normally, the above only applies when copying out of, or pasting into the VNC window.