The backside of the serpentine drive belt, or the smooth side, usually drives the water pump. If the serpentine belt gets oil soaked or glazed, it will slip and not provide the proper circulation to keep the engine cool. And if there is oil on the serpentine belt, it's coming from somewhere so you will need to find out where and fix it before putting on a new serpentine drive belt.
Look for tears or abrasions. If you see any it means the serpentine drive belt is rubbing a pulley flange or bolt as it winds it way around. This will happen more often as the drive belt gets older. If this happens you may need to file a pulley flange smooth or bend something out of the way.
Also look for pinholes and/or bumps. If you see any it means dirt and debris is getting in between the serpentine drive belt and the pulleys. Turn the belt around and see if there are chunks of the ribs missing. You can crank the engine to expose sections of belt as you inspect. A few, small widely spaced chunks are okay, But if there are many and/or close together, replace the serpentine drive belt. Hairline cracks are normal, but if they go into the backing, or flat side, of the serpentine drive belt you will need to replace it.
A good rule of thumb for serpentine drive belts is that if cracks are observed 3 mm (1/8 in) apart, all around the belt, the belt may be reaching the end of its serviceable life and should be considered a candidate for changing. Small cracks spaced at greater intervals should not be considered as indicative that the belt needs changing. However, the onset of cracking typically signals that the belt is only about halfway through its usable life.
If it's time to replace your serpentine belt, check out this helpful tutorial on belt replacement.