I am assuming that your turntable is connected to a pre /amplifier with a "tape out" or "line out", connect the output to the 'line in' on your sound card. Windows recorder should work.
The copies you make will generally not be as good as studio recorded or re-mastered digital copies, but they are going to be as good as you are likely to get them. You could cough up for a sound card that has a high bit count A/D converter, but I do not think you would notice the difference.
Preferably I would look for a program that,
a) Has the ability to remove clicks and pops automatically.
b) Has the ability to view and edit the waveform so you can remove the imperfections manually.
I personally would go for option 'b' but that is because I like to sit in front of my computer screen to the early hours of the morning and fiddle with things to get them as near perfect as possible.
1 Touch Automation.
There is a freeware program called audacity which can do that sort of waveform editing and remove pops and crackles.
I have done some of this transferring; only because I don't want to buy the CD or cannot buy the CD of a LP I own. I have used a Canopus ADVC110 which is a firewire capture device connected to a PC over firewire (of course). The turntable is connected to an amp, the line output goes to the ADVC110 and over firewire the PC gets files in DV format which most software can understand.
System One: Popcorn Hour A200, PS3 SuperSlim, NPVR running on Sempron 3000 (XP), Sony BDP-S390 BD player, Logitech Revue, Pioneer AVR, Panasonic 60" 3D plasma
System Two: Popcorn Hour A200 , Oppo BDP-80 BluRay Player with hardware mode to be region free, Vivitek HD1080P 1080P DLP projector with 100" screen. Harman Kardon HK AVR 254 7.1 receiver, Toshiba HD-A2 HD-DVD player, Roku XS media player
Over the past 4 years I transfered 400 LP's to digital. Used a Project Turntable, with built in pre-amp, through a Creative Audigy2 sound card. The software that came with the sound card included enough tools to subdue clicks etc and also edit the waveform.
Do not under estimate the amount of time this is going to take. Take the time to prepare the LP, play and record the LP, edit the resulting file, split the tracks etc comes to about two hours per LP. Even longer if LP is not in pristine condition. By the time I was finished I had refined my technique somewhat and was recording the whole LP to a single file and doing the editing on that. There is a variety of software available but the only piece of software that tempted me was a program that would split the tracks for you.
Initially I was recording in 24 bit and a high sampling rate to a .wav file. Seriously large files, very slow to work with. After awhile I decided to reduce the recording the settings to CD standard. The mixture of my hearing and equipment that I was playing the recordings on meant that there was no point in in the higher settings.
I am glad that I did it but are quite convinced that a lot of the LP's that I have must have been given to me for surely I would never have brought some of those LP's.