If you're new to recording audio with your computer, it's not exactly obvious how to get started. For the first step, take a look at your computer and see what kind of audio ports it includes. On the back of this desktop PC, the soundcard includes a stereo line input (blue), microphone input (pink), and a stereo line output (green). You also have USB ports, which you can use to hook up a USB microphone or an external sound card.
The port you'll want to use really depends on what you're recording. If you're dictating your memoirs or just recording something around your computer that doesn't need to be high quality or in stereo, you can get away with plugging in a cheap microphone or headset with a minijack plug into the mic input. Look in the box your computer came in and you may find a compatible mic hiding in there.
If you're recording music from something like a cassette deck or CD player, or even an MP3 player, you'll want to use the stereo line input and a minijack cable that has the right connection type on the end that attaches to your audio source. For a portable device, this will probably be a cable with minijacks on both ends, but for your cassette deck, you'll want something with RCA jacks on one end.
Finally, if you're a musician or podcaster looking to make high-quality voice and instrument recordings, you'll want to pick up a USB microphone or a pro-audio external sound card. The mic input on your computer and the mics used for it really aren't designed for quality audio--mechanical noise from your computer can bleed into the recording, and these mics are often made to pick up sounds from all over your room.
Finally, there's software. If you already have some software you're comfortable with, great. If not, I recommend checking out Audacity. It's a free Mac and PC audio recorder you can grab from CNET's Download.com.
Audacity can seem overwhelming at first, but if you open up the preferences in the software and make sure the recording input is the same one you selected in your computer's Sound menu, you should be able to just hit the red record button and see your recording unfold in front of you.
After your recording is complete, you can export it to a universal format such as AIF or WAV. From there, you can drag it into a program like iTunes and burn it to a CD, convert it to MP3, or transfer it to your iPod.