I guess you want to copy from Minibuffer to your system clipboard. Minibuffer keybinding isn't different from other buffers. If in other buffers you use M-w to copy the region, it should also work in Minibuffer. Note that if you niled x-select-enable-clipboard you need to enable it first. I have the following functions in my init.el
(defun copy-to-clipboard()
(interactive)
(setq x-select-enable-clipboard t)
(kill-ring-save (region-beginning) (region-end))
(setq x-select-enable-clipboard nil))
and
(defun paste-from-clipboard ()
(interactive)
(setq x-select-enable-clipboard t)
(yank)
(setq x-select-enable-clipboard nil))
Unfortunately you can't use your mouse to select the texts (ie. to make a region) in helm-mode; you need to set-mark-command (by default C-SPC or C-@) and move your point (ie. cursor). Or just hold the shift and move the point like most other text editors. There is also a mark-word command (by default M-@) that expands the region word by word.
I also recorded an asciinema (because they're fun ) that you can watch it here