In any Bronsted-Lowry acid-base equilibrium, both the forward reaction and the reverse reaction involve proton transfer. Given a Bronsted-Lowry acid or base, how can we determine the identity of its conjugate and correlate the strength of an acid to the strength of its conjugate base?

In any Bronsted-Lowry acid-base equilibrium, both the forward reaction and the reverse reaction involve proton transfer. Given a Bronsted-Lowry acid or base, how can we determine the identity of its conjugate and correlate the strength of an acid to the strength of its conjugate base?