In addition to the rubbing alcohol that was previously alluded to, you can also perform deep cleaning. Now, it should be mentioned that this may or may not be necessary. It really depends on how dirty the grips are and if you feel like removing them (although you can probably get away with leaving them on). Before you begin, you will need to create a mixing solution. To do so, fill up a bucket with warm water and add in a touch of dish soap (it does not take that much).
Stir this solution thoroughly until you begin to see bubbles and foam form. With this solution, go ahead and grab a cloth and dip it inside. Then, simply take that cloth and begin cleaning the grips. All you are really looking to do is remove some of the dirt and grime that is inside. Once you are satisfied with the results, simply allow the rubber to air dry. But, try to avoid doing so in direct sunlight.