Plug the power plug into a wall socket and plug the jack into the green port on the back of your computer. The speakers probably have volume on them but you can change the volume from the computer if you want by pressing Start -> Control panel -> Sounds and Audio devices.
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First to answer your question about the soundcard. Any souncard that supports Dolby Digital 5.1 will work with these speakers so long as the soundcard has a digital output to connect it into the speakers. Most cards that support 5.1 do have this output. But double check to be sure. As for the issue of the home theatre system: If these speakers have multiple inputs and they can decode the Dolby Digital signal then, yes you can connect multiple devices to these speakers. If not, you can purchase an AMP. This is how the setup will work: Computer----- DVD Player---AMP---Speakers TV----------- The AMP allows you to switch between multiple sources such as your theater system and PC and control the volume etc too. If the speakers don't already decode the Dolby Digital signal then you can buy an AMP that will do this. Check that the speakers decode the Dolby Digital signal and check that the soundcard decodes the Dolby Digital signal and has a digital output. I have a feeling that the soundcard you are talking about, decodes the Dolby Signal and in that case you can connect your speakers directly to the soundcard, but you won't be able to connect anything else such as your home theatre system to these speakers. .
you will see in the side of your comp,there is pic of a mic you have plug the speakers there