What you need
A CD-ROM drive capable of recording, or "burning," CDs. Research www.cnet.com or www.zd.net for their recommendations on which burner to buy.
A stack of blank, writable CDs, or CD-Rs. Buy only CD-Rs manufactured to accept audio tracks. Don't use rewritable CDs; CD-RWs may not play on some home or mobile CD players.
A 16-bit or higher sound card on your computer.
Audio cables with two RCA plugs at each end.
An adapter to convert two of the RCA plugs into a single quarter-inch stereo plug.
An adapter to convert the single stereo plug into a one-eighth-inch stereo plug capable of fitting into the the sound card. (You may be able to find one adapter that takes you straight from the RCA plugs to the audio card.)
Software such as Adaptec's Easy CD Creator 5 Deluxe, Magix's Audio Cleaning Lab or Sony's EZ Audio, Nero Burning ROM. I like Nero the best.
Lots of free time. Moving 45 minutes of music could take 65 minutes or more, depending on the speed of the CD player.
How it's done
Connect two of the RCA plugs to the line-out or pre-out jacks on the back of your amplifier or receiver. The amp may have several sets of jacks that carry signals to other devices; consult the manual to determine which jacks should be used for outbound recording.
Use the appropriate adapter to connect the RCA plugs at the other end of the cables to the line-in jack on your sound card. Be sure that you plug into the line-in, not the microphone-in plug.
NOTE: SONY'S EZ AUDIO COMES WITH A CABLE FOR CONNECTING YOUR TUNER/AMPLIFIER TO YOUR SOUND CARD. HOWEVER, IT IS ONLY ABOUT 12 FEET LONG.

Follow the instructions in the software's manual for transferring the music. Essentially it is a two step process. From tape or LP to hard drive and from hard drive to CD.

I generally transfer music first to a CD-RW because that is a convenient way to check if all has gone well.
If you record to a CD-R and something goes awry you will have a created a coaster or a mini-Frisbee because the CD-R cannot be used again.
If you first record to a CD-RW you can listen to the results on the computer's speakers. If all is OK, you can then put a CD-R in the burner and finalize your recording.

If there is a problem, you can fix the problem before you make your final transfer to a CD-R. The test CD-RW can then be reformatted or erased in preparation for its next job.
Consult your manual to determine when to "close" the CD. Closing it prepares it for playing on your stereo or car CD player.

Transferring music from LPs is more challenging than transferring music from tapes.
Your turntable must be properly grounded.
There are problems involved with transferring music from LPs and trying to compensate for the noise on those recordings.
Some inexpensive and popular audio-editing programs can help clean up the recordings, but they may also take the life out of the music.
Dedicated music lovers looking to move music to CDs often rely on very sophisticated sound-editing programs to help them work around the pitfalls of transferring noise-pocked music.
Sound Forge from the Sonic Foundry at www.sonicfoundry.com is one. The downloaded version is $349.
Another oft-mentioned editor is Cool Edit Pro at $399 from www.syntrillium.com/cep the downloaded version. I believe there is a $99 version that many think is quite satisfactory.
If you have a lot of LPs, you may want to try these products, though you may want to first try the demos the companies offer.