In my opinion, you should attempt to understand the case of incompressible fluids before looking at the compressible case, since it's significantly more involved. You can find a discussion of the latter in "Semidirect Products and Reduction in Mechanics" by Marsden, Ratiu, and Weinstein.
For the incompressible case, the result is originally due to Arnold, so that's a good place to learn it. You could also try Section 1.5 of "Mechanics and Symmetry" by Marsden and Ratiu.