Hiya
Yes, very possible. You'll need to connect a tape player to your computer and the leads you'd need depend on what sort of sockets you have. Usually phono, but if your tape player has no 'out' connection you can use the headphone socket. Connect this lead to the 'audio in' of the computer and adjust the sound coming from the tape deck (Control Panel - Sound and Audio Devices - then click the Audio tab). Adjust the volume using the input source that you've chosen.
There are programs available which can record a whole side of a tape/record recognising the gap between tracks as new files. One is RIP Vinyl
http://www.filesland.com/companies/Wieser-Soft ware-Ltd/RIP-Vinyl.html
It isn't very expensive, although there may be free versions of similar programs somewhere.
If you have a choice choose 128kb/s as this gives good reproduction consistent with space used.
Having the mp3s on the comp you only then have to use of the the thousands of burning software to make your CD.