I would recommend one of two ways:
1: If your tapes contain rare or special recordings:
Get this $130 USB tape deck and rip your tapes to your computer. (Note: there's a $100 USB turntable available as well.) Consider using this $35 preamp and noise filter if needed. Plan on spending many long evenings filled with tape swapping and mp3 editing.
2: If your tapes contain currently available mainstream music:
Realize that the above effort is just too much compared to what you get out of it. Spend a while listening through your tapes and make notes of what music you really want to keep, then purchase those songs digitally (Amazon, iTunes, whatever).
3: If you have lots of time and just want to hook up your old tape deck:
In response to the good comment: I've tried some tape ripping earlier which was simply done by hooking up a normal tape deck through the computer's audio-in and recording into a cd-ripping program named "Exact Audio Copy" which also has a line-in recording option. That might be the cheapest way of them all, but also rather time consuming because EAC's ability to automatically split tracks has its limitations depending on the tape's audio quality.
I would choose option #2 unless your tapes contain unique material. This is something I need to do myself, too. So many old recordings from my youth, listening to the radio... oh, the memories :-)