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.

Dan in the comments informs me that if you have vi style key bindings on then the following applies:

1) enter copy mode using Control+b [
2) navigate to beginning of text, you want to select and hit Space
3) move around using arrow keys to select region
4) when you reach end of region simply hit Enter to copy the region
5) now Control+b ] will paste the selection

To enable vi like cursor movement in copy mode put the following in your ~/.tmux.conf:
1

set-window-option -g mode-keys vi

more over what ever you copy, you may dump that out in your terminal using
1

tmux show-buffer

and even save to a file(say, foo.txt) using
1

tmux save-buffer foo.txt

To see all the paste buffers try Control + b #. To dump out the varios buffers on to the terminal or file you may use
1
2
3

tmux list-buffers
tmux show-buffer -b n
tmux save-buffer -b n foo.txt

where n is the index of the paste buffer.