So, you're hooked up:
1. Your turntable is stable, has a cartridge installed, and the tonearm is balanced.
2. The turntable's grounded cables lead to an RIAA phono preamp.
3. The preamp is plugged into your soundcard or outboard A/D converter.
4. The converter is plugged into your computer by USB or Firewire. Drivers for the converter are installed on your computer.
Great! Time to start recording.
I use Soundstudio (shareware) for Mac and the free, open-source Audacity (Windows, Mac, and Linux) to record. Acoustica and Acoustic Labs are good shareware programs for the PC.
You can find tons of audio programs for Windows, Mac, and Linux at Hitsquad, a great musician site with a huge shareware repository.
Before I record, I'll wipe the record clean, lube it up with a little Gruve Glide (antistatic spray, and I love the buzz -er- scent). De-gunk your needle with the little brush thingie that came with your cartridge, and prepare to spin!
I try to record at 24-bit, 48kHz, which is the max setting for most USB converters. This gives slightly above CD-quality recordings. You'll probably adjust these settings in your driver's control panel and the recording program's preferences.
If your software has a graphic 'input levels' indicator (above), play a track or two in order to test your signal strength before hitting the 'record' button. Adjust the levels (volume) until the peak volume is hitting in the yellow zones without clipping (red zone).
I generally record the entire LP side as one take, then slice it up in the editing program, copying and pasting into separate tracks. I don't like to stop and start the turntable, and on some albums, the breaks are so miniscule that each song flows together.