How is the leader of a nation selected?

First of all, I mean absolutely no offence. And I am quite unfamiliar with Islam. Please be kind and forgive me for any offence. I was reading about the Taliban. What I understood is that elections are not in conformity with some religious law. So, they denounce elections. Tibetan Buddhists have Dalai Lama. They select the next one using their methods, which too I am unfamiliar with. I understand many Muslim majority nations have elected leaders. And Saudis have a monarchy. According to religious rules, how is the leader selected? And what do you call him?