I think you'll unfortunately be left unsatisfied since there is no "simple" answer due to the way clipboards work in x11 and the historical baggage a lot of terminal apps drag with them (everyone did text-copying differently before ctrl-c and ctrl-v became ubiquitous).
A nice thing you can do in Vim though is to make the default clipboard the system clipboard like this in your .vimrc:
set clipbaord=unnamedplus