If you are restricted to only using screen, then the solution is like this (also works for non-split or horizontally-split screen windows):
crtl+a [ to go into copy mode
- navigate using the arrow keys or hjkl keys (vi-style)
space to mark the start of your selection
space to mark the end of your selection, copy to screen's buffer and exit copy mode
ctrl+a ] to paste
Fancier movement keys (e.g. move to start of line/buffer) can be found here.
If you are not restricted to using the vanilla OSX terminal + screen, you may want to try some terminal that natively supports vertical splitting and run a separate screens on the left and right vertical panels. One terminal that supports this is iTerm2.
With terminal-supported vertical splits you can copy-paste using the mouse as-usually. You will still have to use the screen shortcuts to copy stuff from the screen scrollback buffer.
If you go with iTerm2, then you may also consider ditching screen altogether and switch to this version of Tmux. Tmux is a replacement for screen. The customized version above seamelessly integrates with iTerm2. I.e. opening/closing new screens is handled with iTerm2 shortcuts, and the scrollback buffer is directly accessible without having to switch to some special tmux mode.