There are at least four verbs that mean "to do" in Japanese: する, なさる, いたす, and やる. What is the purpose of each, and when is it appropriate to use them?
する is the most general, neither too polite nor too formal. やる is more informal and could tend to lean toward rudeness. Note that やる cannot replace する in sino-Japanese compounds. For example, 電話する could not change to 電話やる. なさる is keigo (尊敬語), used for someone "higher" than yourself. いたす is humble keigo (謙譲語), referring humbly to yourself or others in your group.
Usage-wise, there is not much difference between them, except for what I noted above.