Connect your cassette deck or player to your computer. To do this you will need a stereo RCA cable with a mini-jack. Connect the stereo RCA end of the cable to your cassette deck, using the red for the right audio and white for the left audio. Then connect the mini-jack end of the cable to your computer's audio-input jack. This will allow the audio from your cassette to travel to your computer.
Record the audio from your cassettes onto your computer using audio-editing software. Some quality audio-editing software includes Audacity, Garage Band and Cubase. When you make a new project in one of these programs to record into, make sure that you set the program to record from the audio input. You can usually set this preference in the program's system preferences, settings or options menu. Once you have that set, hit Record in the program and then hit Play on your cassette player. The audio from your cassette player will now be recording into your computer.
Export your cassette music from your audio-editing program to an audio-listening program such as iTunes of Windows Media Player. To do this you can click on the export or share menu bar that is common in most audio-editing programs. In this menu there should be an option to convert the audio or send it to iTunes or Windows Media Player. Click on that option and within a minute or two your music should be listenable in your media player.