The following will work only if
vim --version indicates that you have
+xterm_clipboard feature. If not, you will have to install extra packages or recompile vim with that feature added.
There are actually two options for this:
copies to the "usual" clipboard buffer (so you can paste using Ctrl+V, right click and select "Paste" etc), while
copies to the X11 selection - you can paste from this buffer using middle click.
"+ work both ways. So if you have selected some text in another application, you can paste it into vim using
"*p and if you have copied some text (using, say, Ctrl-C) then you can paste it into vim using