How to get into math research as an undergrad?

Hello, I've completed 2 years as a compsci major and will be starting my math major next semester. After some wandering about I feel fairly confident that I want to go down the pure math researcher / professor route (or at least try to). I heard research is pretty important for phd applications. In my country (Argentina) the best school combines the undergrad with a "masters" so its 6 years, which i feel like is enough time to get something going (the title is still bachelors though lol). So, how would I go about getting into research? I have some basic background from my cs studies, though I understand I might need a bit more to contribute. Just to get an idea, what would be steps I need to take to get started? Thanks