Step 1: Recall the meaning of conjugate base.
In the Bronsted-Lowry idea, an acid gives away one proton, which is one $H^+$. What is left behind is called its conjugate base.
Step 2: Write the simple rule.
To get the conjugate base, remove one $H$ from the formula and make the charge more negative by one.
Step 3: Start with the given species.
The given acid is $H_2PO_4^-$. It has two hydrogens and a charge of minus one.
Step 4: Remove one hydrogen.
Taking one $H$ away from $H_2PO_4^-$ leaves the $HPO_4$ part.
Step 5: Adjust the charge.
Removing $H^+$ makes the charge go from minus one to minus two. So we get $HPO_4^{2-}$.
Step 6: State the answer.
So the conjugate base of $H_2PO_4^-$ is the hydrogen phosphate ion. \[ \boxed{HPO_4^{2-}} \]