In what ways did Martin Luther go about trying to achieve his goals?
This is a good question. When you talk about Martin Luther, you also need to talk about the Protestant Reformation, which was a significant movement in Europe that shaped the world.
Martin Luther wanted the Catholic church to reform its theology and practice. For example, when the church started to sell indulgences, Luther had enough. Here is a jingle that was popular in Luther's day:
"A coin in the coffer rings, a soul from purgatory springs."
In light of this corruption, Luther decide to put up his 95 Theses. He took a stand and did not let his conscience be bound up by tradition. He also started to write many theological tracts and he certainly used the printing press to his advantage. He also translated the Bible into German.
His fight was in many way an intellectual one. I suggest that you read a few of his works to get a sense of the polemical nature of his writing. Start with these: Babylonian Captivity of the Church and the Bondage of the Will. Finally, Luther was also politically savvy as he had some of the wealth support his cause.