The SM58 doesn't use phantom power but you need a preamp of some sort to get the signal up to line level (right?) so you can hook it up to the soundcard. Soundcards have a mic input as well but the are not intended for use, at all

Also, the mic input on a soundcard is designed for computer microphones, which works diffrently than regular mics. I don't know any other names on "cheap" stand-alone preamps than the ART Tube preamp but that one is highly recommended by many here. The ART preamp and an SM58 mic should be a great voice setup, at around US$150 though (again, right?). Any other suggestions for stand-alone preamps?
Plug the preamp's line output to the line input on your computer's soundcard and the do what John said.
If you have an MD recorder, you can just plug the preamp into the line input and you'll have a fairly portable setup. You'd still need power for the preamp but as dannymix suggested, you can bring it to singing lessons. The tracks on MD can be recorded to the PC through either the line out (if the MD recorde has one) or the headphone out. If you use the headphone out, you'll need to be carful with the level or you'll end up with a too quiet or a distorted recoring. Also, the quality may be lower if you use the headphone out than the line out.
Then when you're hooked on recording like the rest of us, you might want a better soundcard for higher quality but that's the next step.
/Ola