How does the winner take all system of the elctorial college work?

"Winner-take-all" in the electoral college itself is pretty much unavoidable, because we have no provision in the Constitution for two or more people each being "partially President".

The winner-take-all provision that most states used to govern how that state's electors vote is entirely avoidable, though, and a few states (notably Maine and Nebraska) apportion their electors in a more equitable way. However, in the majority of states, all the state's electors are pledged to vote for the winner of the popular vote within that state. It means, for example, that the Democratic candidate for president is all but guaranteed California's 55 electoral votes even before the Democratic candidate is named, and the Republican candidate for the election of 2020 can, even now (in 2017) pencil in Texas' 38 electoral votes in his or her column.

This, incidentally, is how a candidate for president can lose the electoral vote while winning a majority of the popular vote: In 2016, several of the states in which Clinton won tended to vote overwhelmingly Democratic (inflating the popular vote margin while not making any difference to the electoral vote), while the majority of states in which Trump won were decided much more narrowly.