Doing computational chemistry requires (1) the technical know-how to use special software and computers and (2) the knowledge to understand what the software is telling you.
On that second point, there’s a lot of math and physics behind the theories of chemistry—and its great stuff! But before you dive into studying a lot of formal math and physics, its good to know what you’re working towards. Chris Cramer (a professor at U. Minnesota) is a computational chemist who has written a computational chemistry textbook and put a bunch of free video lectures up on Youtube that explain the concepts behind computational chemistry at a level that most students can understand. If you’ve taken general chemistry, an organic chemistry course, and a couple semester of calculus (multivariable calculus is great, but not absolutely necessary), these videos are great background and inspiration. As you move through the video series (49 total — a full course!) the material gets rich, but if you follow along you should understand the spirit of it.