I use Audacity to record the sound and save it to a WAV file.
I make a copy, and work on the copy. I use Audacity to break up
the huge WAV file into its various tracks and work on the tracks
individually. That's easier on the CPU and if you screw up its not
such a problem.
There's a useful denoise filter on Audacity I sometimes use, but
most of the real work is done with the Gnome Wave Cleaner. It's free.
http://gwc.sourceforge.net
The GWC has just about everything I need; noise filters, declickers,
etc. After a track is clean enough, I use Audacity to amplify it to its
maximum below the clipping barrier.
If you're picky like I am, its a long and distressing job. Some records
just can not be cleaned. I only clean records that there are no CDs for.
Otherwise, its not worth the time and aggrivation. Good Luck!