I started doing this as well.
I simply use the tape-out on my amplifier to the line-in on the computer - ie just as if it was a recorder.
You will need software to do the recording. There are a few on the net varying from about $30 - lots for the more professional ones. I have used Audiotools and can highly recommend it. I think it is around $30 which will get you the upgrades. There is a good web page and a bulletin board. Answers to questions are promptly answered - the support is excellent. The URL is:
I also downloaded a program called POPFIX which was quite effective in reducing pops and clicks. Again it was around $30. There are others as well. You may want to explore some of the download libraries such as Lycos etc. To shop around
The software to burn the CD should come with the CD-writer.
Any good luck and I hope the above helps.