Assuming your turntable is already connected to your stereo, connect the phono ends of your phono-plug-to-mini-plug cable to the left and right tape outs of your stereo, and the mini plug end into your soundcard's line in. There's not enough signal to come directly out of your turntable into your soundcard, thus the need for the phono preamp in either the separate unit or within the stereo.
Using either your PC's recording control dialog or the control program that came with your soundcard, select the line input and bump the volume control all the way up. Do the same with the play control dialog for line input (you may want to move the main control volume bar down unless you're adjusting volume on the speakers themselves).
If you're using a stereo amp, check your connection by playing anything through your stereo system and see your volume display moving up and down. For digital recording (unlike analog), you want to record 'hot' enough to just miss 0 db. Otherwise you will hear clipping in your wav files, which, when unwanted, is an ugly type of distortion.
If you aren't getting enough volume through the connection described above, or don't have tape out RCA/phono jacks to connect to, you can use a quarter-inch-to-mini plug, connecting it between your headphone jack and the soundcard's line in jack. Turn any equalization, frequency turnover, loudness controls off, and make sure your balance is set to 0, or equal balance between left and right. Take care, because with the volume turned way up you can overload your soundcard! It's a little trickier to monitor the recording; just remember that when you're adjusting the master volume on your stereo, you're adjusting the input to your soundcard.