Hi,
Just wanted to add (in case there was any confusion) that you need to record the LP in real time - as if you were recording it to cassette, but this time the cassette is the computer software that records it to a file and then is ready to be burned to a CD.
Play around with the input and output levels of your computer and turntable to get the best end result as well - it is easy to record it with either too much signal or not enough - the best way that I find to do this is to record a bit and then play it back and compare that to a professional CD recording - if the levels are about the same then you have probably got it just right =)
I use Adobe Audition to record things, but if you don't want to pay for software then there are plenty of free programs around. I then use CDex to convert the recording to MP3 and then Nero to burn the tracks to disk.
Have fun! The cool thing about copying all your LPs onto CD is that you get to listen to them all at the same time!