How did Napoleon reform laws in nations he took over?
Napoleon did not do this in the same way in every country he conquered, but the basic idea is that he tried to impose the ideas of the Enlightenment in his empire.
Napoleon often tried to destroy the old order in the conquered countries, just as he had helped to destroy it in France. He reduced the power of the Catholic Church and of the old nobility. He instituted laws that were based on Enlightenment ideas such as religious toleration, economic freedom, and the equality of people (at least men) in the eyes of the law. He had the other countries adopt the ideas of the Napoleonic Code, with things such as jury trials and more transparent legal systems.
In general, Napoleon tried to destroy the old systems of the countries he conquered and replace them with systems that were more liberal but were also ultimately subordinate to Napoleon himself.