Many countries have a different system for choosing a prime minister, but I will assume that you are asking specifically about the process used to choose the prime minister in the United Kingdom. The prime minister begins as a member of parliament, but will then be appointed head of their party by party members. When a general election is called, they will then go up against the leaders of other parties to try and gain the most votes. If there is a majority for their party, they will become prime minister.