To clean a record the right way you need a special brush. You can get it at any audio shop. You clean it by doing the OPPOSITE of CD cleaning - go in circles, following the grooves. Otherwise, you'll scratch the grooves (btw, record grooves are where "groovy" came from). Store records vertically, not stacked, otherwise the grooves in the lower records get flattened out. Test the needle on the record player on a record you don't care about first. If it's bad, you don't wanna wreck a good record. If it's bad, you need a needle cartridge. This is a REAL dicey area - you can easilly pay $400 and more for a single needle. You need to find the balance of affordability and sound quality - the really cheap ones will make your records sound a lot worse than more expensive ones.
It's pretty easy to record from record player to another source. Plug the record player into the PHONO plug on the back of your stereo receiver. You can now record on tape, CDR, minidisc, or whatever else you have plugged in. What I generally do, since my receiver is hooked into my computer, is run the record player through the receiver, record to mp3 files, then compile them on a CDR.
If you want to record them, do it quickly. Every time you play a record you wear it out a little bit. Records don't sound nearly as good on even the 10th spin as they do new.
You'll also have to learn to walk softly unless your player is shock mounted, because players don't have anti-skip
