The conjugate base of any acid #HA# simply the acid MINUS a proton, #H^+#; when we do this for #HA# we get #A^-#. Likewise the conjugate acid of any base #A^-# is simply the base plus a proton, #H^+#, to give #HA#. Mass and charge are conserved.
To use sulfuric acid as an example, we start with the #H_2SO_4# formula; less a proton, this gives #HSO_4^-# as the conjugate base, and the conjugate base of #"bisulfate"# is #"sulfate"# ion, #SO_4^(2-)#. All I am doing is exchanging protons, #H^+#, and conserving mass and charge.
Can you tell the conjugate bases of the following acids: #HClO_4#; #H_3PO_4#; #NH_4^+#; #NH_3#; #NH_2^-#; #HC-=CH#; #NH^(2-)#?