How to convert LPs to CDs.
Records and tapes wear out, and there is no better way to preserve your music than to convert your tape and vinyl collection to CD. Fortunately the process has become both easy and inexpensive.

You will need a computer with a sound card and a CD-RW drive (CD burner) capable of burning audio CDs, a tape deck or turntable, proper cables (more about them later), and the right software.

A comprehensive tutorial on how to do this right.

One suggestion
astranger: The line in jacks on a sound card are not designed to work with the low output level of a record player. Record player outputs have a much lower level than a tape or CD player. I'd recommend always plugging the record player into the "phono in" input on your amplifier, and plugging the "tape out" output from the amplifier into the sound card. Then setup the amplifier as if you were going to copy from record to tape, and follow the rest of the tutorial from there. You should get less noise and better sound than if you connect the record player directly to the sound card.
jones: thanks astranger...that's a great tip. anyone else have any good knowledge to share? this is what i'm doing for my dad for his b-day!
mtness: If you're going to do this, make sure your amplifier, record player, and computer are all plugged into the same circuit in the house. Often the ground can vary from circuit to circuit which can easily add a hum to your recording.