Matlab is an incredibly powerful software, in my opinion, I think nothing is better than go through the official guide by Mathworks, just grab a random tutorial/example from the web to get started, have a look at the relevant toolboxes' documentation for your related field, and make use of "help" functions as much as possible.
If you need a book for reference, on the webpage of MathWorks has a nice overview of MATLAB books for mechanical applications (FEM, heat transfer etc.), you can go through it to find out the books that relevant to your research: