Is it permissible to take money from Google in exchange for users clicking on advertisements displayed on the website, which direct them to the websites of the advertising companies?

The described contract is a permissible ju'ala (reward-based contract) provided that the advertisements are free from anything unlawful or from assisting in it. This is a type of ijara (leasing/hiring) where some ambiguity in the work is tolerated, and it requires the monetary compensation to be specified. The proof for the permissibility of ju'ala is the Almighty's saying: "And for him who brings it is a camel's load; and I am responsible for it," and there is a consensus on its permissibility. It is necessary to know the content of the advertisements so that they are not for prohibited things, due to the Almighty's saying: "And cooperate not in sin and aggression."