Answer
Bronsted-Lowry acid: $H_2O(l)$
Bronsted-Lowry base: $NH_3(aq)$
Conjugate acid: $NH_4^+(aq)$
Conjugate base: $OH^-(aq)$
Work Step by Step
According to the Bronsted-Lowry definition,
Acid: proton ($H^{+}$ ion) donor
Base: proton ($H^{+}$ ion) acceptor
In the reaction, $H_{2}O$ is the acid because it donates a proton.
$NH_3$ is the base because it accepts the proton.
A conjugate acid is any base to which a proton has been added. So, $NH_4^+$ is the conjugate acid.
A conjugate base is an acid from which a proton has been removed. So, $OH^-$ is the conjugate base.