How will socialism be established?

Socialism can only be established by a vast majority of people deciding it wants to establish socialism. Therefore, the World Socialist Movement puts forward the socialist case so that people can decide for themselves.
Once the vast majority makes the decision in favour of socialism, then it will elect socialist representatives or delegates to prove its majority, and to serve as a temporary focal point to administer the elimination of capitalism and the creation of socialism. But it won't be, and could not be, the elected representatives or delegates who create socialism, it will be the people of the world as a whole.
The vast majority of the people of the world are working class, so socialism will be established by the working class. It also means that ordinary people will have to do all of the work required. The capitalist class isn't going to do it, and professional socialists (whatever they might be) aren't going to do it. The only way to establish socialism is for people to work for it.