I think a good starting point for changing someone else's political beliefs is to be able to clearly state what their beliefs are, and the reasoning behind those beliefs, in a way they will agree with.
I'm no Trump fan, but I live in a red state and have occasional discussions relating to political issues. I just don't see all the racism, ignorance, and hate that so many people on the left assume is behind voting for republicans. Honestly, I hear more hate and disrespect from the left than I do the right. I hear a lot of comments about how horrible/stupid/evil Trump supporters are, and how such terrible people need to be dealt with, so we can live in a tolerant country without hate... How people can express such hatred, while believing they are on the side of tolerance and acceptance, is an amazing thing.
I think that before spending too much time figuring out how to educate people that disagree with you, you need to actually be able to articulate the point of view you disagree with in a way that is reasonable to the people you disagree with.