I don't know the best way but one way would be to select text in your web
browser with [Ctrl][C] copy it, then paste it [Ctrl][V] into a notepad like
application. But sounds like you would need two documents open at once. One for
translating each little phrase and another for the whole document as it is
built.
But you could open another document and select copy each phrase translation into
that document as you go along as well.
Hope this helps. I don't know the name of the Linux equivalent to note pad.
[Ctrl][C] and [Ctrl][V] usually work within any text program including on web
pages.