How do I respond to arguments disparaging the religion or the prophet?

*This is intended to be a canonical dupe-target for this class of question, which I see come up way too often.* --- I've encountered an argument, either in person or from a website, which claims that something I believe about the prophet or the religion of Islam isn't true. This argument most likely comes from a non-Muslim, and I think he's trying to make me leave Islam. They have backed up their claims with numerous references, including hadiths and verses from the Qur'an, as well as from a variety of scientific resources. I have faith that there is no God but Allah and that Muhammad is His messenger, and I believe that Islam is the right path, but I don't know how to defend my faith against these arguments. How should I answer?