I'm about to graduate and enter a 1-year master's program. I don't really know any professors, and I've never done research. How can I get involved?
Is it too late for me to get involved in research? 


No, your timing is excellent. 


  how do I actually get started?


Presumably you know what fields interests you. One of those fields should probably be your research field. If possible, opt for a master's degree with a research focus (rather than an entirely taught degree). Opt for any research focused modules. Opt for any modules in your chosen field. Conduct any coursework on research problems. Establish whether you really want to do a PhD.

In parallel, start searching for a PhD supervisor. That supervisor can be located anywhere in the world that you are willing to live. Selecting a supervisor is most likely covered elsewhere (e.g., https://academia.stackexchange.com/a/10878/22768), so I wouldn't discuss further.