i m assuming that the tmux prefix is Control+b and that you have emacs style key bindings on
1) enter copy mode using Control+b [
2) navigate to beginning of text, you want to select and hit Control+Space
3) move around using arrow keys to select region
4) when you reach end of region simply hit Alt+w to copy the region
5) now Control+b ] will paste the selection
you can navigate the text using the emacs style navigation key
Control+p, Control+n, Control+f, Control+b etc.