Only certain lizards can climb and cling to surfaces, notably geckos (which is an entire infraorder of lizard). They are able to do so because of tiny hairs on their feet call setae. read more
The simple answer is their feet are like Velcro. The slightly more complicated answer is that their feet have microscopic hairs called Seta or setae as plural, these hairs work through Van der Waals force. read more
Until a few years ago scientists did not know, though they proposed several conflicting theories. read more