I've done a similar project. I had an old radio program recorded on a cassette and wanted to archive the music onto a CD with track markers.
I used audio editing software--Sound Forge--to get the audio onto my computer for editing.
Patch your cassette audio into your sound card on your PC. Set up the input so you can monitor the sound. Then start a new project in Sound Forge (or other audio editing program). Fine tune your project settings then start recording. Once you have one long wav file recorded you can then get to work on splitting it into separate tracks.
In Sound Forge you can place markers. You basically separate the audio file into tracks by using markers. Place markers where you want songs to start and end. Once the audio file has been completely marked you then convert all the markers to regions. Finally you then export the regions to a specific folder on your PC.
In that folder will be your tracks as wave files, exported from Sound Forge. You can use various softwares to convert those wave files to Mp3 or other formats.
Then use your CD burning software to format and burn your CD with tracks.
That's a quick overview of how I took a few old cassettes of mine, separated the music into tracks, and burnt them onto a CD.