Couple ways to do this.
mkdir ~/Documents/Logs sudo nano /usr/bin/terminalLogging sudo chmod 755 /usr/bin/terminalLogging
Put this into the file:
#!/bin/bash /usr/bin/script ~/Documents/Logs/`date +%m.%d.%y-%H.%M.%S`.$$
In the terminal options, set to run:
sh terminalLogging
man script
Get http://iterm.sourceforge.net/
Shell > Log > Start / Stop