When light strikes an object, some of it penetrates the object, and some of it is reflected and reaches your eye. When an object is wet, more light penetrates the object, so less light is reflected. As a result, less light reaches your eye and so the wet object looks darker. Read on for a more detailed explanation.
Most frogs and toads breathe (and take in moisture) through their skin through a process called cutaneous gas exchange, but they also have lungs with which they breathe. During the time they stay submerged under water or buried in soil (such as during hibernation) they ONLY breathe through their skin.