Depending on the quality you want you can:
If you don't mind spending $140, try this audio Tape deck for the PC:
http://www.thinkgeek.com/electronics/audio/7a8d/
Presumably, if the actual tape hardware is decent, this would give you the best quality capture since you wouldn't get any outside interference, but its far from the cheapest solution.
The cheap route is to take any cassette player like a sony walkman and use any 3.5 mm male to 3.5 mm male cable to connect your tape deck head phone out to your computer's audio input. Then get your hand on software, there is a ton of them out there, and you can record it as a wav. I would first record it as a wav and then if you want, you can convert it to an mp3 from the wav or you can edit the songs and then burn them as tracks to a CD.
If you want to ensure the higher quality recording, I would use a higher end tape deck and use a better quality sound card or maybe a USB Video/Audio capture device and get your hands on a short good quailty cable. The setup is still the same except you might go from an RCA out to RCA in or 3.5mm audio in on your sound card. Since you plan on getting your band back together, you might consider getting some semi-pro software with good hardware to get some decent recordings from your band. You might look at companies like M-Audio.
Software:
If you want to go free, try Audacity for recording from a CD, dvd or any audio input and then editing. It may not be professional yet but it has some great tools and effects for a quick job.
If you have an Apple, you can try out the new GarageBand software, which is part of ILife. It has received some decent reviews and its really neat because it supports Ipods and Podcasting, which is a neat feature for up and coming bands.
M-Audio has come out with Session as an aswer to GarageBand. Its supposed to have a lot of the same or similar features as the Apple software.
B-Smack already mentioned Sony's Sound Forge Studio which is good for 'budding professionals' according to Sony, but they also have Sound Forge 8 for professionals for $299.
Obviously there are other options for software and hardware. You might consider checking out websites like:
http://createdigitalmusic.com/.
Good luck!