What do I need? A rather broad question dependent on how you intend to approach the recording process. Do you intend to go pc based or use casette or hard disk based multitrack recorders? Each has his own advantages and disadvantages.
With multitrack hard disk recorders, you often just turn them on and start recording. They usually come with internal effects and allow you some form of editing and volume/pan/mute automation. You lose out on visual onscreen editing, except if you're using those high end Rolands (ex. VS-2480) and Korgs.
With pc recording, aside from software, you will need a multitrack soundcard. You can get by with consumer soundcards but they will often have less than desirable sonic performance and are usually only stereo input, regardless of the number of inputs on the breakoutbox. Don't believe me? Try to select the aux in and line in simultaneously. If you intend to record more than 2 tracks, you need a serious soundcard.
Then there's the software question. Google around for Audacity and Kristal Audio Engine for freeware. There are other shareware options such as Multiquence, then there are the big boys starting with Adobe Audition, Sonar, Cubase, Nuendo, or if you prefer the Mac platform, Digital Performer and Logic Audio. M-Audio sometimes has Pro Tools LE bundled with some of its soundcards - note that PT LE will only work with M-Audio hardware.
Once you decide which of the 2 paths to take above, this will determine the ancilliary equipment you will need such as mixers, preamps, and mics.