Take a clean washcloth, rag, or paper towel and spray it thoroughly with Armor All. A washcloth is preferable for its texture, taking into consideration how delicate a vinyl record can be.
Place your record on a smooth, unsoiled surface. Squeeze out the rag or washcloth and gently wipe each side of the record, reapplying more Armor All as necessary.
Dry off any excess wetness from the Armor All with a dry towel or washcloth. Place the record on your record player and put the needle on it to test whether or not the record is still skipping in the same part of the song. If it is, another way to clean it is to keep the record on the turntable, and place the Armor All coated rag flatly, and gently, on top of it. Move the needle over so that the record turns without actually playing. Hold the rag so it gently moves across the entire record. The rag should then be able to catch any dirty spots that you have missed before.