How to get involved in research early, build a CV for academic medicine, and explore PhD and fellowship opportunities.
Talking to the professors can definitely help in this. Most of the professors have completed PhD or are persuing it, some of them do research and can help and recruite some specific students. 
Start by joining small research projects with your professors or mentors, Curiosity matters more than experience at first.
Attend conferences, publish case reports, and network. Over time, this builds a solid CV and opens doors to PhD or fellowship paths.