PuTTY's copy and paste mechanism is by default modelled on the Unix
xterm application. The X Window System uses a three-button mouse, and the convention is that the left button selects, the right button extends an existing selection, and the middle button pastes.
Alternatively, with the ‘Windows’ option selected, the middle button extends, and the right button brings up a context menu (on which one of the options is ‘Paste’). (This context menu is always available by holding down Ctrl and right-clicking, regardless of the setting of this option.)