How do you write a balanced equation for reactions that involve acids and bases?

Acids are characterized by being producers of hydrogen ions, H^+. Bases are characterized as being producers of hydroxide ions, OH^-. The two react to form water:

H^+ + OH^- \rightleftharpoons H_2O

That is the basis of all equations involving acids and bases. The other ions in the mixture are "spectator ions". They aren't changed in the reaction. You can add them to the left side and their salts on the right side and re-balance the equation. For example if Hydrochloric acid were used, you'd have chloride ions, Cl^- or if sulfuric acid were used, you'd have sulfate, H_2SO_4. If, for the base, you had sodium hydroxide, you'd have sodium ions, Na^+. If the base were magnesium hydroxide, you'd get magnesium ions, Mg^{+2}. You can write equations like this:

HCl \rightleftharpoons H^+ + Cl^-

H_2SO_4 \rightleftharpoons 2H^+ + SO_4^{-2}

NaOH \rightleftharpoons Na^+ + OH^-

Mg(OH)_2 \rightleftharpoons Mg^{+2} + 2OH^-

The salts, which are simply combinations of the cations (positive ions) and anions (negative ions) might be:

MgSO_4 \, or \, Na_2SO_4\, or \, MgCl_2\, or \, NaCl

the combined equation might be

HCl + NaOH \rightleftharpoons H_2O + NaCl

or

H_2SO_4 + Mg(OH)_2 \rightleftharpoons 2H_2O + MgSO_4