Dan,
Well, I pretty much already explained how, but let me get a little more in-depth with it.
Go to System > Devices and Feature Codes > Hunt Groups > HG XXXX: Set Group Call Pickup to Yes
Go to System > Devices and Feature Codes > Phones > Ext XXXX > Programmable Keys: Hopefully you know how to figure out which programmable keys you have available on each phone. Set it to Park/Pickup and in the Selection column put in the extension of the Hunt Group.
Alternately you could go to the keymap itself and hard program a Park/Pickup key for each Hunt Group, but then you would need a different keymap created for each department if they aren't all going to want to have access to the other departments pickup group; wasteful but it works. Typically a seasoned technician would create a keymap that uses Programmable Keys for as much as possible to allow for flexibility.
Done.
Thanks,
TE