We will prove a result of Feldman and Moore that a Borel equivalence relation on a Polish space which has countable equivalence classes can always be realized as the orbits of a Borel action of a countable group. Then we will prove a result of Kechris that any equivalence relation induced by a Borel action of a locally compact Polish group is essentially countable, meaning there's a Borel reduction to one with countable equivalence classes. Thus, an equivalence relation induced by a Borel action of a locally compact Polish group can always be Borel reduced to one induced by a Borel action of a countable group, i.e., there's a reasonably definable way to decide one equivalence (belonging to the same orbit) given that we can decide the other.