I took a look at their joystick on the jammaboards.com website. Since it's a 4 / 8 way joystick, it uses an actuator that you flip over underneath to make it 4 or 8 way. In order to flip it over you need to remove the e-clip at the bottom of the metal shaft of the joystick itself. You would do the same to install it onto a control panel. Flip it upside down and you will see it. Use a small flat head screwdriver to pry it off.
It will look something like this when taken off:

Then simply pull the joystick out from the base from the top. Be sure to note where everything is while you pull it out for reassembly. Then install the base, and simply put the joystick back in and secure it with the e-clip again.
P.S. - Obviously you can ignore that comment made about cutting the control panel in half. Not many people realize that they were once a newbie and they should treat others with the same respect. We welcome newbies and the majority of us are all happy to help.
~ DeLuSioNaL