Use a portable cassette player. Portable cassette players, like the Walkman, were gigantic sellers in the 1980s. Millions of them still exist and function today, and can be found very inexpensively at a thrift store. If you have a portable cassette player, it can be used to easily transfer music into your computer, which can then be burned onto a CD. You will need to obtain a 3.5 mm to 3.5 mm stereo cable to do it. These can be found in most electronics shops, and look like a typical headphone cable but with a plug on both ends. Make sure the plugs have two black rings on the metal part, not just one. Two black rings indicates they transfer a stereo signal, ensuring your CDs sound proper.
Plug one end of the cable into your portable cassette player and the other into the "Line In" jack on your computer sound card. In a pinch, the "Microphone" jack will work as well, but may cause quality issues.
Run a RCA to 3.5 mm Y-cable from your cassette deck in your stereo system to your "Line In" jack on your computer. Cassette decks are frequent additions to many existing home stereos and can even offer a higher fidelity playing source from which to record your digital version. RCA to 3.5 mm Y-cables are a little bit more rare than the 3.5 mm to 3.5 mm cable, but can be found at your local electronics or music stores at a reasonably inexpensive price. Note, however, that the same ring-rule applies to the Y-Cable. Make sure the 3.5 mm end of it has two black rings and not just one.
Choose your recording method and software. Once your cassette source is hooked up, it is a matter of what you choose to make your digital recording as well as process. You can simply play the whole tape and record using the built-in system sound recorder and sort it all out later, or you can use a sound editing package to tweak and edit the sound of the recordings you make. An excellent free tool for sound editing is Audacity.
The other consideration is an all-at-once recording versus recording individual songs and saving them into individual files. Generally, it is easier to save the individual songs as separate files instead of going back through and chopping the recording up into smaller parts.
Once you have a digital recording of your cassette, you can burn it to a CD. Most CD burning software can burn in either data or audio format. Make sure you burn to audio format or your CD player may not recognize that you have a music CD inserted. Once you burn the CD, it can be fun to use a printed CD label that looks like the album cover for the cassette. Most recordable CDs can hold up to 70 minutes of music before running out of space.
The actual choice of software for burning a CD is a matter of preference. Most manufactured systems come with at least one CD burning package.