"I want to connect my PC up to my JBL column speakers in the living room so I can listen to Internet music there but I'm not sure how to go about it. I suspect I need to run cable from the output jacks on my soundcard into my Stereo amplifier to get the "push" needed to drive the beasts. Am I on the right track? Currently my SoundBlaster sound card has headphone type output plugs which run into some home outlet powered PC type speakers."

You are correct. Heck, that was easy. I love it when the people asking the question already have the correct answer. Even though speaker outputs of computers have enough power to drive small speakers they probably won't drive anything like a home stereo speaker (though there can be exceptions - try it). This also applies to the headphone outputs of little Walkman type devices. Normally you'd never connect the output of an amp designed to drive speakers to the input of a stereo receiver, mixer, or any other line level gear. But in these cases the power is low enough that you can do it. Remember, the input impedance of a line input is generally very high, certainly much higher than any speakers. When connected to the little amps that drive these small speakers the increased impedance significantly lowers the output power and the speaker output begins to behave much more like a standard line output would. So basically you are just connecting a line out to the line in of your receiver or mixer and then using your normal amp to drive the speakers.