Step 1: Create the Dividers
Open the Terminal and execute the first command to create a divider on the left or the second comment to add one on the right:
# Left side
defaults write com.apple.dock persistent-apps -array-add '{tile-data={}; tile-type="spacer-tile";}'
# Right Side
defaults write com.apple.dock persistent-others -array-add '{tile-data={}; tile-type="spacer-tile";}'
Execute the command as many times as you like; a divider will be created each time. You will not, however, see them added before your eyes.
Step 2: Reset the Dock
Reset the dock to see your new divider(s):
# Reset the dock
killall Dock
Once the dock is reset, you'll see spacers which you'll be able to drag throughout the dock.
Why dividers aren't a common feature of OSX yet is a question I can't answer. Luckily we can abuse Terminal to make our dividers though.