Dampen a cloth with rubbing alcohol and wipe it around the record, going with the flow of it. I know they used to have some roller things that would clean them but I really won't know if they still sell them. They were a roller with a squirt thing for the alcohol but I bet the cloth would work just as well.
PS. If you really want to listen to your music in all it's glory you might just think of downloading it off the Internet. Records sound kinda scratchy.
One more thing, once you get them clean if you want to save you music, you can record them onto the computer and save them as mp3 files.
Here's how: Go to
http://audacity.sourceforge.net/ to download a free recording software that is awesome.
Then get your old turntable and a line in cord. Plug from the line out /or/ speaker plug in the turn table to the line in /or/ microphone plug on your computer.
Let the whole thing play and then save your project. You can open your project later and edit it, cutting the tracks so that you have one song at a time.
Hope this is helpful.
Recorded and clean old records for my dad.