Each star is assigned an integer (starting at 1), followed by " G. " (or occasionally followed directly by a "G" without a space), and then the Latin genitive of the constellation it lies in.
They were assigned according to the stars' positions in epoch 1875.0, and over time are affected by Precession of the Equinoxes.
Gould's catalogue includes 66 constellations (some of which are also covered partially or fully by Flamsteed numbers): † 30 Doradus and 47 Tucanae are Bode numbers, not Gould designations.
Additional designations were heavily dropped and forgotten, i.e. Kapteyn's Star was originally called C.Z.
V 243 by Gould himself, But these designations are extremely rare to find outside of that aforementioned article.