Linux is above my pay grade, but Windows is as simple as the Mac way. I'll break it down into easy-to-read steps, since no once likes reading a big block of text.

1) buy (if not owned) an audio signal converter. For example a Behringer UCA-202, or similar device. I honestly can't find anything as good or similar for nearly the price, aside from other Behringer things with small differences
2) take your tape deck (whatever you use to play cassette tapes) and wire the "OUTPUT" section to the UCA's "INPUT" selection
3) open/download and open Audacity or a similar recording program on your computer. In Audacity, there should be a picture of a mic (I might have an old version, so new ones may be different), and a drop-down tab. From that tab should be an option called "USB" something, depending on the name of your device. Select that one
4) Start playing the beginning of your tape, and hit the red circle universally known as "record." You should start seeing blue lines
5) One recording starts, slide the input volume slider (speaker shape on the far upper left) to a lever so that the blue shapes appear a reasonable size
6) OPTIONAL STEP: Listen to the recording so far at your normal computer volume and see how it sounds. If you don't like it, raise or lower the volume. If you do, restart.

These instructions work on Mac, Windows, and Linux. Also, here's instructions for installing Audacity, though I'm sure there's a million online for that.

1) Go to their website and download it. Here for Windows, Here for Mac, and Here for Linux.
2) Once you've installed Audacity and made it a Desktop icon, etc, it should tell you you need to download LAME for MP3. LAME can be found here, though I don't feel like breaking it up for you

Good luck!