Instead of throwing them out after light cleaning tasks, like drying your hands, save used paper towels to use again. Simply let them dry in between uses.
Add more dish towels to your kitchen to help you conserve paper towels. With more cloth towels nearby, you'll be more likely to reach for them when drying dishes.
Sponges are ideal for sopping up spilled water and other liquidy messes and can be reused for these tasks much better than paper towels, so keep some around.