First of all, fire up Audacity, and then open your sound monitor (right-click on the speaker icon on the taskbar and select Recording Devices). Make sure the sound levels don't go over the top of the bar, as that causes "clipping", and will make your recording sound crappy. If you are clipping, you can adjust the volume of your inputs using the software bundled with your sound card. Most generic cards are Realtek cards, so I'll demonstrate with the Realtek HD Audio Manager. This is generally accessible by double clicking an orange colored speaker icon on the taskbar. A window will appear, go to the tab labeled "Line In". Set the recording volume to a level that won't clip (I've got mine set at 15), and adjust the playback volume to something that sounds good.
Now that you've got that out of the way, put on a record, clean it off, and hit play. In Audacity, make sure you're recording. Let it play all the way though the section you want; you may find it easier to record the whole album at once, and split up the individual tracks afterward while trimming off any excess.
After you're recorded what you want, you can use several tools to clean up your recording. The most useful tools are under Effects > Noise Removal. Use them at your discretion to clean up your recording. In order to apply the effect, make sure your whole recording is selected, this is easily done by pressing Control + A.
can help you get your recording as hot as possible before you export it. Use discretion as too much compression takes all of the dynamics out of your recording and generally makes it sound crappy. In most cases modern recordings make heavy use of compression, which is why the latest Cage the Elephant album will sound much louder than, say, Led Zeppelin IV.
Once you've got your recording the way you want it, you'll obviously want to export it. Go to File > Export, and a new window will appear. Select the formant you want with the drop-down menu, give it a name, and hit "Save". A new window will appear, this will allow you to edit the details of the file. Fill in what you want and hit OK, and you're done!
If you want to go even further, you can burn your newly ripped songs to a CD using your preferred CD/DVD burning software, or Windows Media Player, iTunes, etc. I like to use InfraRecorder http://infrarecorder.org/
, it's free and does a good job, plus it has a cool smoke animation when it burns a disk :).
So that's it! Thanks for reading my instructable, if you have any questions or things that I might have left out, feel free to point them out, I'm always open to constructive criticism. Have fun ripping your records!