When I started out I was basically stumbling around for code that worked. Things got a lot easier for me once I sat down and actually understood broadcasting.
The rules are: 1) scalars always broadcast, 2) if one vector has fewer dimensions, left pad it with 1s and 3) starting from the right, check dimension compatibility, where compatibility means the dimensions are equal or one of them is 1. Example: np.ones((2,3,1)) * np.ones((1,4)) = np.ones((2,3,4))
Once your dimensions are correct, it's a lot easier to reason your way through a problem, similar to how basic dimensional analysis in physics can verify your answer makes some sense.
(I would disable broadcasting if I could, since it has caused way too many silent bugs in my experience. JAX can, but I don't feel like learning another library to do this.)
Once I understood broadcasting, it was a lot easier to practice vectorizing basic algorithms.