Rinse with water. Distilled is best, but COLD tap will work in a pinch.
For cleaning something like a finger print, I buff with a soft, almost warn-out, 100% cotton t-shirt or 100% cotton diaper (cloth diapers are great for dusting, waxing cars, etc.)
If its still skipping, first try a fill method:
For treating scratches that cause skips: Rain-X in the automotive department. 2 DROPS FILLS the scrates. Spread with a cotton ball(don't press). Let dry for 20 minutes. Buff with the above mentioned t-shirt or cloth diaper until ALL the haze is gone and the surface looks transparent. One treatment will last for years. (At one time Armor All was thought to work, but it chemically reacts with the polymer surface of the disk and will degrade it over time. It also has to be retreated while the rain-x treated disks haven't needed retreatment after 16 years (the oldest treated one)
If its that doesn't do it, your looking at a resurfacing method that polishes away a thin layer of the surface. I don't recommend this unless you are sure that nothing else works.
I've used the Rain-X treatment as needed at home (5 or 6 disks) but mainly us it at work to repair data CDs/CDRs for the job ("hey AR, my 6 year old used this as a frisbee") and customers - I've been a professional computer geek (todays title is "IT Manager") for 14 years.
If you can see a scratch in the platter itself or can see it from the top, you no longer have a cd: you have a coffee coaster.
Hope this helps.