Experimental observation of matter/antimatter in the universe Ordinary matter and antimatter have the same physical properties when it comes to, for example, spectroscopy. Hydrogen and antihydrogen atoms produce the same spectroscopy when excited, and adsorb the same frequencies. The charge does not make a difference in the potential (regardless if it's generated by a proton or an antiproton) nor in how the positron behaves in this potential (being its mass equal to the mass of an electron)
How can astronomy evaluate if a far galaxy is made of matter or antimatter, given that from the spectroscopy point of view, they behave in the same way? In other words, how do we know that an asymmetry exists between matter and antimatter in the universe? 
 A: Matter and anti-matter behave in the same way with respect to electromagnetic interactions, so we could not distinguish the two by electromagnetic observations.
It was mentioned in the other reply that annihilation from the contact of matter with antimatter would produce a signature gamma radiation that would be easily observable. That is true, but things are not that simple. It has been calculated that matter and antimatter could be kept separated by a type of Leidenfrost layer between them that would be supported by a relatively slow rate of annihilation (Collective effects in diffuse matter-antimatter plasma: I, II). That rate could be so slow and the layer so small, that it could be practically unobservable in cosmological distances. I am not trying to support a theory that would claim that there are great amounts of antimatter in the universe, but there are some who do.
Apart from all that, one way to distinguish between the two could be the detection of neutrinos. In a supernova of an antimatter star for example, the neutrinos that we would get would not be the same as the ones from a normal matter supernova, I suppose.
A: To be a little pedantic, nobody has yet done precision spectroscopy of antihydrogen, though the recent success in trapping it at CERN (all over the news this week, paper here) is an early step toward that. It's possible that there are small differences in the spectrum of antihydrogen and hydrogen, though these differences can't be all that large, or they would be reflected in the interactions of antiprotons and positrons with ordinary matter in ways that would've shown up in other experiments.
As I understand it (and I am not an astronomer) the primary evidence for a lack of vast amounts of antimatter out there in the universe is a lack of radiation from the annihiliation. We're very confident that our local neighborhood is matter, not antimatter, which means that if there were an anti-galaxy somewhere, there would also need to be a boundary region between the normal matter and antimatter areas. At that boundary region, there would be a constant stream of particle-antiparticle annihilations, which produce gamma rays of a very particular energy. We don't see any such region when we look out at the universe, though, which strongly suggests that there aren't any anti-galaxies running around out there.
