I had the same question when I was in college and did not know what to do. But now, with some reading and experience, I know how much I don't know. Here's a short introduction to get you started:
You should know that when somebody talks about computational materials science, they are talking about using a computational technique to solve a problem in materials science or metallurgy. These computational techniques could be FEM, DFT, Phase-field Modelling, Molecular Dynamics or anything else.
A good way to think about these techniques is that typically, they are specific to a particular length scale. DFT and MD are "a few atoms" scale. Phase-field modelling is in the "large nano to micron" scale. FEM is a much larger length scales.
The foundation of all of these computational methods is mathematics for obvious reasons{:target="_blank"}. If you want to understand and use the techniques mentioned above, you might need a little mathematics: Numerical Methods, Multivariable Calculus, Linear Algebra, Statistics.
Of course, no one expects you to be an expert in any of these mathematical techniques (at first), but after a first-level reading of what these techniques are and how they work (check out Wikipedia), it would be a good idea to take a MOOC and get started. Khan Academy{:target="_blank"} is a good starting point.
I prefer watching videos, but if you wish to read some textbooks on this subject, check out these books: Computational Materials Science: An Introduction by June Gunn Lee and Introduction to Computational Materials Science by Richard LeSar.
The third component is programming. I am assuming you have beginner level prior experience in writing code. Start with the most basic exercises (arithmetic, loops, functions etc.) For starters, try this{:target="_blank"}. Learn to use GitHub. You can learn how to use it in a couple of hours! Host all of your code on GitHub.
If you've got this far (in the post as well as IRL), pat yourself on the back.
When I first heard about computational materials science as a subject area, my starting point was learning to use OOF2{:target="_blank"}. Installing it comes with a slightly steep learning curve (if you have never used Linux before); the developers make it easy to set up and use the package. Try it!
Going one step ahead, you can also check out QuantumEspresso{:target="_blank"} and LAMMPS{:target="_blank"}. I am familiar with both but have not used them enough to give you an informed opinion. Nonetheless, I would recommend you check them out.
If you don't find resources, search on YouTube (filter by playlists for courses). Check out Library Genesis{:target="_blank"} and SciHub{:target="_blank"}. You can learn a lot by exploring sites like Quora and StackExchange. You may also find my GitHub repositories{:target="_blank"} helpful.