Convert a cassette tape recording to digital format
Use a 3.5 mm stereo-to-RCA cable from the RCA out of the cassette tape deck to the Line In jack of the sound card.
Select Line In as source for your recordings.
Then grab Audacity and record/cut your tapes. Keep the the results in a lossless format (e.g. WAV - or compressed as Monkey's Audio or FLAC to save space) for further processing before converting to MP3.
Note: Audacity requires the LAME MP3 Encoder for MP3 conversion.
Note: This would not be a fully digital remaster as you're still using an analog tape player.
I used a Roland Edirol UA-25 to interface the cassette deck of my stereo to my computer (Mac), but only because I had one (Musician). I could have just as easily have done it using the line in on the standard sound card (usually the blue jack).
I recorded using Audacity to record the audio and also do some post processing. However I could not get it completely hiss free as they were very old recordings of a relative who had passed away, so there was no way to reproduce it.
Fortunately, I work for a very large media company in the UK and their sound department did an amazing job of reading the audio I had recorded and removing more noise than I could possibly using the equipment I had. Admittedly, the sound studios contain millions of £ worth of sound processing hardware and I was very lucky to get this done for free.
If you can afford to get a professional to do this then the reproduction should be much better than you could do on home equipment.