I also added a short sound clip, so you can get an idea of the sound quality. I didn't run it through any filters, so that's what it sounds like directly off of the record.
Step 1: Stuff You'll Need
2.) A Phonograph (a.k.a. a Record Player, I'm using a Beogram 8002)
3.) A Phono pre-amp (In my case a Rotel RA-8408X)*
4.) A Stereo RCA Audio Cable
5.) An RCA to Mini-Jack adapter
6.) A Computer with recording software
You can easily pick up records at places like DI and second hand stores, or the like.
If you don't have a Phonograph, you can find them online, in second hand stores, ect.
The RCA cables can be easily acquired at Radio Shack, other electronics stores, or online stores (Monoprice http://www.monoprice.com/home/index.asp is my favorite)
Pre-amps can be found online, the cheapest one I've found is this one http://www.mcmelectronics.com/product/40-630. The pre-amp is necessary because of a special equalization curve, called the RIAA EQ curve, that was applied when the record was recorded (RIAA stands for the Record Industry Association of America). The curve limits the lower frequencies and boosts the higher ones. A pre-amp then limits the high frequencies and boosts the low ones, creating a good-sounding replication. If you didn't use a pre-amp, you'd end up with a poor quality recording.
Finally, on to the the computer and software. Basically any computer will do, you just need to have a line-in input, and sufficient hard drive space to store your recorded music. Having a more beefy computer helps with ease of editing and exporting the final product. The software I use is called Audacity http://audacity.sourceforge.net/, it's free, cross-platform, and open source. Plus, it comes with some handy plug-ins that you can use to clean up your final recording. I'm using the beta, if you're a beta kind of person then go ahead and use that, but for others I would recommend the stable release.
*Recent releases of Audacity include the RIAA EQ Curve (and many other EQ curves) with the Equalization effect by default, so a pre-amp is not necessary.
Step 2: Set It All Up
Next, find the output of your pre-amp. It may be labeled as "Tape (Rec Out)" or similar. In my case, it's label as "TMONITOR 1". Take your RCA to mini-jack adapter cable and run it from your amp to your computer. You should plug it into the "Line-In" input for your computer, because it will capture stereo signals, and the "Mic" input will only give you mono. Generally, the line-in will be colored blue. Some devices have a start up spike, so I would recommend that you connect it to your computer after you've turned everything on.
That's it, you're all set up to start recording, at least as far as hardware goes.
Step 3: Software and Configuration
Step 4: Cleaning Your Records
Step 5: Recording - At Last!
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.
Compression 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!