RemapPrefixKey

In your .tmux.conf

# remap prefix from 'C-b' to 'C-a'
unbind C-b
set-option -g prefix C-a
bind-key C-a send-prefix

or from the command line

tmux unbind C-b
tmux set-option -g prefix C-a
tmux bind-key C-a send-prefix

The latter is important as, while I'm happy with C-b ordinarily, if I am in a tmux on my Thinkpad, ssh into my HP N40L, and open a tmux there, I need to remap the prefix key, but if I ssh in from a terminal that is not a tmux, I don't need to remap. I then also

tmux set -g status-bg blue

so that the tmux in a tmux is clearly distinguishable from the outer tmux. (Note that I'm not running a tmux in a tmux on the same machine: one tmux is local, the other remote.)