NOTE: There is a newer and better version of this article at http://www.nsftools.com/misc/TapeToCD.htm.
Here's how I recently transferred a cassette tape to a CD using the ahead Nero Wave Editor software. I'm using version 1.0 of the Wave Editor on Windows 98, so if you're using a different version or a different operating system, the instructions may vary somewhat. You can also find some excellent instructions about converting tapes to CD at cdrfaq.org (this is what I used as my starting point).
Essentially, the process is to hook a tape player up to the sound card on your PC, record the songs/music on the tape to WAV files on the computer, and then transfer the WAV files to a CD. More detailed instructions are below.
Step 1: Connect your tape player to your sound card
If you have a tape player with a "line-out" jack, you should really use that, but you can use the headphone jack in a pinch. Whatever you're using, connect it to the "line-in" plug on the back of your sound card. Almost every sound card in the world uses 1/8th-inch plugs, although your line-out/headphone jack may or may not be the same size (make sure you're using a cable with stereo plugs -- if there's one little ring around the metal part of the plug it's mono, if there are two little rings it's stereo). Play a little bit of the tape to make sure it's coming out of the PC speakers -- if it is, you've hooked everything up right. NOTE: if you don't hear anything, there's a possibility that your "line-in" volume is just muted. Open up the Windows volume control (Start - Programs - Accessories - Entertainment - Volume Control), go to Options - Properties, make sure that "line-in" is one of the volume controls that is checked, and make sure that the line-in isn't muted.
On your tape player, make sure that any of the balance or bass/treble dials are set in the middle, so you'll get a true recording of the music. Also make sure any "bass boost" settings are off, so your final recording isn't muddy.
Step 2: Record a song
Open up the Nero Wave Editor and select the menu option Audio - Record. Use the default Sample Rate of 44100 Hz and 16-bit, and make sure that "Stereo Recording" is checked, and click OK. The Recording Console will initially start at a paused state. While the console is still paused, play a little of the tape, and make sure that the Input Level indicator goes up and down with the music that's playing. If not, you may have to change your audio input settings. You can do this by clicking Cancel, opening the Windows Sound Recorder (Start - Programs - Accessories - Entertainment - Sound Recorder), choosing the menu option Edit - Audio Properties, clicking the Recording Properties button (with the little microphone on it), and making sure that "line-in" is selected in the recording control (if it doesn't appear as an option, go to Options - Properties and select it as an available volume control).
Once your indicator is indicating that it's picking up the music you're hearing through the PC speakers, fast-forward to what seems to be to be the loudest part of the music that you're recording, and adjust the volume on your tape recorder so that the indicator peaks at just under the 0-Db Input Level mark when the music is the loudest. Ideally, you want the whole song to stay in the -20 to -10 range on the Input Level indicator.
After you have the volume set properly, rewind to just before the beginning of the song, start playing the tape, and click the "Record" button on the Wave Editor Recording Console (the button with the little red circle). After the song is over, click the "Pause" button on the Wave Editor again (just to the right of the Record button, designated with 2 vertical lines) and click the "OK" button to insert the music you just recorded to a new Wave Editor file. Make sure you have a few seconds of "silence" from the tape before and after the music track, so start recording a little before the song starts and stop recording about halfway through the break between songs.
Choose the menu option File - Save As to save your recorded selection as a WAV file.
Step 3: Clean up the track
Now that you've created a WAV file, you'll want to clean it up a little before you send it to CD. Here's how:
1. Select the entire track (menu option Edit - Select All) and "Normalize" it to 0-Db by choosing the menu option Volume - Normalize.You may also need to adjust the equalization of the music at this point, but I'd recommend burning the WAV file to a CD first to see how it sounds. Sometimes trying to boost the bass or the treble using your PC speakers as a guide will make your final recording sound too bright or too muddy. Test it on a real stereo (or multiple stereos, if you're really particular) before and while you equalize.
2. Select a small amount of "silence" from the beginning or end of the track (drag the mouse over the part you want to select), and choose the menu option Enhancement - Noise Analysis. Set the Reduction Level to 70% and click OK.
3. Select the entire track again (Edit - Select All) and choose the menu option Enhancement - Noise Reduction. Click OK. This should remove a good amount of the tape hiss that came over with the track (you never really want to set the Reduction Level in the previous step to 100%, because that can create a lot of strange audio artifacts in the track -- 70% is usually good enough).
4. Trim all but just a little of the "silence" at the beginning and end of the track by dragging the mouse over it and choosing the menu option Edit - Delete.
5. Choose the menu option File - Save to save the file again.
Step 4: Burn the WAV file to a CD
Just use your favorite CD-burning software to do this (probably Nero Burning Rom, if you've got the Nero Wave Editor to begin with), using the instructions that came with the software. If you're transferring an entire tape, you'll want to convert each song separately as an individual track, and then burn all the tracks to the CD.
Of course, you could also convert the WAV files to MP3 files at this point, if you wanted to keep everything on your computer. There are plenty of pieces of software you can download (many of them free) that will handle the conversion for you. Try tucows as a starting point if you're not sure which software to use.