I have done all kinds of work that required some kind of matrix calculus in one form or another. There are of course all kinds of references (sibling links to my favorite), but I have found that more often than not really the best way to get the results you want is just to calculate them yourself. The work involved is usually tedious but trivial. But working through it goes along way to help make some sense of the various identities that come out. In looking at an identity one may see a transpose here, an inner product there, but not be able to assign any importance or distinction to any particular term at first glance. Working through a few calculations help with this.

EDIT: I suppose I should also say that I never "learned" matrix calculus either, in the sense that I internalized the various features unique to matrices under derivatives and integrals. The calculations I refer to above are crude, naive ones in the scalar notation under whatever coordinate system seems appropriate.