If I plug speakers or headphones into the headphone jack in my laptop,
they work fine.  However, if the laptop is in the docking station,
then I can only hear sound through the speaker on the docking station.
 The headphones and speakers do not work.  How can I troubleshoot this
problem?

Depends on the brand of the laptop and which docking station you use
and which OS you run , usually there is a setting either in the bios
of the machine or the 'setup' program that comes with the computer
that allows you to change certain settings depending on whether the
machine is used as a laptop or a 'docked' machine

Reinstall the sound drivers for the laptop. If you have XP on it, the
laptop might be using the default drivers which don't really recognize
the docking station audio plug. I had the same issue with my Dell
laptop. Bothered me for the longest time.