Hi James,
Looks like you've been a little misled by someone or something about the idea of soundcards and preamps. A preamp is just a device that boosts the level of the mic's output from mic level (really soft) to line level (usably loud). Even some of the best and most expensive pre-amps in the world are just stand-alone preamps without any soundcard-like feature.
Soundcards, on the other hand, are simply devices that convert your analog sound into digital data for your computer to read and understand, and back from the computer to analog for you to hear (output -- to your speakers / headphones). Of course, cheap on-board soundcards on computers give you a horrible signal-to-noise ratio, hence home recording enthusiasts have begun to use prosumer-grade soundcards, aka recording interfaces, most of which now come with a built-in preamps and even features like phamtom power and even phase correction in some cases. Hope that makes sense.
You have two options now:
Either you swap your ART tube MP for an interface that gives you onboard pre-amps, or you may need to purchase an audio interface (which may also have built in mic preamps) or a simple mixer with a built-in USB audio interface, to connect your preamp to. Here are some examples of both:
Mixer with USB interface:
http://pro-audio.musiciansfriend.com/product/Behringer-XENYX-1204USB-USB-Mixer?sku=485369
Audio Interface (soundcard):
http://www.sweetwater.com/shop/computer-audio/audio_interfaces/
You get decent ones in the range of 150 to 200 USD that should get the job done. You also have things such as the Blue Icicle, but I'd personally recommend that you stay away from that because it doesnt give you much flexibility in terms of line-inputs and balanced outputs for monitors.
Now the cables (any brands should do. dont buy the cheapest, but dont even looks at the super-expensive ones, in my opinion. buy something about one or two grades higher than the cheapest and you should be OK).
A) If you use your ART Tube MP:
Use this type of a cable to connect the mic to your Tube MP:
http://accessories.musiciansfriend.com/product/Musician's-Gear-LoZ-Microphone-Cable?sku=338001
Use either another piece of the same cable (mic cable) or the following cable (instrument / guitar cable) to connect the line out of the Tube MP to the line-input of the interface that you buy. Usually, the interface may have a stereo line input, but since the tube MP output is mono, you could simply buy a mono cable and plug it into either (ideally Left) input of the sound interface / mixer.
http://accessories.musiciansfriend.com/product/Live-Wire-Advantage-Series-14-Straight-Instrument-Cable?sku=330470
And then finally hook up the interface or the mixer to your computer via the USB cable that is provided.
Do note, if you're not particularly attached to that ART Tube MP, you may conveniently bypass that stage (return it or exchange it for either the USB mixer or a USB / Firewire interface) and directly plug the mic into either the mixer or the interface using the same aforementioned mic cable. I haven't used the ART Tube MP myself, but I hear that most budget preamps don't differ much in quality, so its not like the onboard preamps on the mixer or the interface would be audibly worse in anyway. But that's upto you.
Hope this helps.
EDIT:
Note that you may need to configure these devices in Audacity or in Windows (or Mac). The Behringer USB Mixer I hear is plug and play.. but other interfaces like those of PreSonus and M-Audio may need to be installed and configured. So don't be zapped if you plug it in and nothing shows up :)