Note: this page is is hopelessly out of date, but people keep linking directly to it. The correct place to read my index of articles on audio CD-R is here, while 12 Step Recovery From Audio CD-R Problems contains my most recently version of the comments below.
While I'd like to give details that could help out everyone here, you have to realize that the exact mechanics are very much dependent on what sound card you have. See, in order to be able to work with the LP's sound, you first have to apply some sort of analog to digital conversion in order to get it into a form the computer can deal with. The easiest way to add an audio A/D converter to your system is with a sound card; all of them I've ever seen have a phono jack line-level input. You can't just plug your LP into this, mind you; LPs are recorded with an equalization system that is usually referred to as the RIAA curve, and if you try and use the direct output from your phonograph into the sound card it will not only sound funny but probably not be loud enough to hear properly, either. What you need to do is find something with a phono input on it (be it a receiver, preamp, or dedicated phono amplifier), feed your phonograph into it, and use the line output (typically you get one of these from the tape output jack on the equipment) to drive the sound card input with. You'll usually need an adapter to plug standard audio RCA jack outputs into the mini-phono, headphone style jack. These come with many sound cards, or you can buy one at Radio Shack (just make sure you have a stereo converter cable; just because it has two RCA plugs doesn't mean the mini- phono plug is stereo, count the black rings at the tip and make sure there are two of them, if there's only one it's a mono plug).
If you get all that working right, playing an LP will play on your computer's sound card. You may have to find a volume level program to turn the line input up loud enough to hear (these are scattered all over the place in most Windows sound setups, or there may be a DOS utility around if you're there). In any case, you'll need to find that volume level adjustment eventually to make sure you're not overloading the sound card and playing too loud. Avoiding clipping this way is a fine art I can't say I've mastered myself yet; I just play it by ear at the moment, turning it up until it seems "loud enough" and turning it down if it sounds distorted after I record something.
Hope your sound card is a 16 bit stereo model, because otherwise you're out of luck (OK, it's possible to sample without a card like that and then increase everything in software, but I don't recommend that). Finding the recording software is your next goal. Windows comes with a little application called Sound Recorder. If you change its settings so it creates 16 bit stereo files at 44.1Khz and save to a WAV file, that should be usable to make a CD track out of. This recorder is simple enough to learn how to use, and it has some rudimentary editing functions. The only one I use is the ability to chop off the portion before or after the editing cursor; for things that I recorded too much of, I can find the break and slice things. One barely documented feature that's very handy for this is knowing that if you move the editing cursor somewhere, you can then fine adjust it in tenth of second increments with the left and right arrow keys. At CD resolutions, you can usually see any significant break on the waveform display. One thing that is a problem with using this little application for serious work is that, unlike the media player, it loads the entire WAV file into memory before it can work on it. You get your typical 5 minute song lasting 50MB, and unless you've got 64MB of RAM it takes a long time to do this.
The best resource I've found for looking at the entire market was again from PC Magazine, this time from the multimedia article in the March 28, 1995 (Vol. 14 No. 6) issue. The 29 boards reviewed all got hooked up to that audio review favorite, the Audio Precision System One. You get frequency response graphs and a host of other statistics. The boards they liked are the Turtle Beach Monterey ($399) and Tropez ($249), which I suspect are good performers. Avoid their cheaper Monte Carlo board at all costs; I got robbed buying that waste of silicon based on Turtle Beach's reputation, and found the sound quality approximately equal to your average Fisher-Price children's record player (you know, the one with the bright plastic records and the groove so big you can almost hear the music from looking at it). Accordingly, I'm not keen on giving more money to TB. Another weakness with their cards (and many others on the market) is compatibility--most software programs assume cards are Sound Blaster compatible; the Monterey isn't, and while the Tropez is supposed to be, I have yet to meet a non-Sound Blaster card that worked with every piece of software out there. No, if you really want Sound Blaster compatibility, buy a Sound Blaster. The Sound Blaster Cards from Creative labs not only work with everything, they have sound quality that is top notch for computer sound cards at their price. I use their AWE 32 board myself (the current incarnation, the AWE 32 PNP that I haven't tried yet, goes for about $250 everywhere). The frequency response is almost dead flat from 20hz- 20Khz, S/N is up over 78dB (it doesn't get much higher than that in noisy computer environments), channel seperation is up over 83dB, and the distortion is at CD player levels. Hopefully they haven't screwed the card up in the last revision. For a bit cheaper, the Sound Blaster 16 Value Edition retails for under $100, and all you lose for the price difference is a bit of upper end extension (response is another fraction of a dB more down at 20K) and a considerably higher THD; it's still very acceptable for most purposes. Other differences between the cards are related to downloading instrument samples to the card and DSP effects; those are the things that justify the "32" in the name of the more expensive card. You also get more cables and software thrown in on the AWE32 that you'd have to get separately with the SB 16, like a hydra- headed audio cable for your CD player (and I always prefer to buy the board that already comes with all the cables you need). I really wouldn't recommend any cards on the market but the ones from Creative Labs; not only are they the standard and work great, they sound about as good as you're going to get in a computer as well.
As far as specifics on using the software that comes with the SB cards goes for recording things like vinyl, I always use the DOS version of their utilities. Call me paranoid, but when I've got something feeding at high frequency in real time to my computer, I don't want to be in a multitasking environment where some process can interrupt that flow and screw the sound up. So while the Windows Sound Recorder may be wonderful, I do not trust it to accurately record critical items. The DOS utilities that come with the two cards I have are the same (at least as far as recording goes). There's a utility called SB16SET (yes, it's called that even on the AWE32) that lets you adjust the relative volume levels of all the card's inputs and outputs; it takes some time to get set just right, you'll want to experiment with it for a while before doing any serious recording, but the default was fine on my system for most recordings. SB16SET is a bunch easier to use if you load your DOS mouse driver before running it. If you click the Save button before exiting the program, the settings you changed will get reloaded by your computer's AUTOEXEC.BAT (the card's installation program runs SB16SET /S there to restore them). In order to record to a WAV file, logically enough you use the RECORD utility. The somewhat cryptic command line looks like this:
You can change this into a batch file by creating one that looks like this:
Playing the WAV file back to hear how it sounds can be done with the corresponding PLAY utility, which isn't quite so complicated (you need only give it the file name). Note that in order for these utility to run, you need to have loaded all the various SB driver programs that the card software installs in your CONFIG.SYS and AUTOEXEC.BAT (you can delete some of them and everything but the play and record utility will still work). I usually record an entire album to a chunk of hard drive in DOS, check them out to make sure they all sound right (that the level is set correctly), and reboot into Windows NT to do touch-up editing with the sound recorder; after that, off go the tracks to Incat for burning.
What is more of a concern is what happens to anything you have to pass through your sound card before it hits the CD-R, like a vinyl recording. I did some testing with my Sound Blaster AWE32, taking the analog feed from my CD-ROM drive, using the A/D converter on it, and playing it back again using the computer's D/A converter. Compared to the original CD, the differences in sound quality were small but noticable. I'd peg them as being slightly smaller then the difference between an average original CD and an average remastered version of it; not a huge difference, but some things seem to lose something on the inferior recording. I can live with that level of sound degradation in order to get things onto CD that weren't available there before.
Now, when you're talking about playing vinyl LPs into the system, I don't think I'm especially qualified to discuss that much. I just got my first turntable for this project; while I've used other people's over the years, I've never actually owned one myself. The Denon DP-23F (I got mine used, current production versions run about $399 with cartridge) is very good turntable for the turntable illiterate, even having a row of buttons for start, stop, etc. like a CD player. Don't know if I'd buy one new when you could get a simiarly priced one from Rega, Dual, or Thorens, but compared with the 20 year old Dual I had been borrowing before it's a masterpiece. I still don't like LPs; I don't like handling them, I don't like having to clean everything constantly, and I don't like the way they sound. Accurate frequency response and low distortion are what push my buttons, and I won't give either up for any of the things LPs are supposed to be better at if you play them correctly. With this turntable, though, I find records are now usable and can sound pretty good, where I couldn't stand them before. Maybe there's hope for me as a vinyl listener yet. Anyway, feeding the turnable output through an Adcom GTP-400 preamp phono stage into the sound card to digitize things ended up producing a CD that I'd be hard pressed to tell from the original vinyl; I couldn't hear any difference over the surface noise that easily masks the kind of distortions I'm used to hearing the sound card introduce in its A/D conversion. Perhaps others might with their own equipment, but I didn't hear anything from the vinyl that's getting lost in the translation with any of my moderately priced equipment.