You can copy text from an MSYS window to the clipboard simply by selecting the text you want to copy. As the text selection changes the clipboard is updated to contain the selected text. To paste text from the clipboard into an MSYS window either click the left button while holding down the Shift key, or else click the mouse wheel (clicking anywhere in the MSYS window will do). Pasting text you've copied from MSYS into another program (e.g. Microsoft Word) is accomplished using the normal mechanism(s) supported by the other program (e.g. Ctrl-V).
An alternative way to copy output from MSYS is to redirect it to /dev/clipboard. E.g. you can copy the contents of file foo to the clipboard using |cat foo > /dev/clipboard| and then paste it elsewhere.