What is the conjugate base of ${\text{OH}}^{-}$?

To find the conjugate base of a species, remove one proton (${\text{H}}^{+}$) from it.
$${\text{OH}}^{-}-{\text{H}}^{+}={\text{O}}^{2-}$$
Thus, the oxide ion (${\text{O}}^{2-}$) is the conjugate base of the hydroxide ion.