You vote for the party first and foremost, not for any individual politician. Instead of voting for a local representative, you vote for a single party to represent you at a national level. That party then gets a certain number of seats based on how many votes it got. As a result, voting for a minor party that only gets 10% of the votes actually makes sense, as it then gets 10% of the seats in the parliament. In such systems there usually aren't single parties with a majority, but coalitions of parties with varying viewpoints.

There are many mixed systems that use party voting, but also link parties to specific candidates. However, the system the previous comment described sounded more like party-list proportional representation.

For a large federal system like the US that has both local needs and far less regional differences than people realize, replacing the House and Senate with a party-list would both unify the country and destroy the power of duopolistic party elites. At the same time, the state and local elections could use any number of systems that focus more on candidates. It wouldn't prevent a fascist like Trump from taking over, as Israel is a modern example of a party-list country under fascist control, but it would've required him to build a party as a politician rather than take over one of the big two.