Represent the ionization of acetic acid in water using a chemical equation. Label the conjugate acid-base pair?

HC2H3O2(aq) + H20(l) ---> C2H3O2^1-(aq)    + H30^1+(aq)
   acid               base              conj. base            conj. acid
Here acetic acid is the proton donor (acid), and after it has donated the proton, it now has a negative charge so it has the potential to pick up a proton. Thus it is now a conjugate base. In one sense, any negative ion is a potential base. Good bases (conjugate or otherwise) come from weak acids. The larger the pKa, the better the ion is as a base.
The most common 'base' is hydroxide ion which comes from water!
                 H2O  +  H2O  -------->  H3O^+  +   OH^-
                 acid       base                 conj. a       conj. base
Most acids will begin with H, e.g., HOCl, take away the H and you get the conjugate base, OCl-
OCl- is a base because it is a proton acceptor. All salts are associated with a conjugate base, some are good (hydroxide ion) some are very poor (sulfate ion).