Identify the ions present in the solutions before mixing: AgNO_3 dissociates into Ag^+ and NO_3^- ions, and NaCl dissociates into Na^+ and Cl^- ions.
Write the full molecular equation showing the reactants and products: AgNO_3 (aq) + NaCl (aq) → AgCl (s) + NaNO_3 (aq).
Write the complete ionic equation by breaking all strong electrolytes into their ions: Ag^+ (aq) + NO_3^- (aq) + Na^+ (aq) + Cl^- (aq) → AgCl (s) + Na^+ (aq) + NO_3^- (aq).
Identify the spectator ions, which are ions that appear unchanged on both sides of the equation (Na^+ and NO_3^- in this case).
Remove the spectator ions to write the net ionic equation, which shows only the ions and compounds directly involved in forming the precipitate: Ag^+ (aq) + Cl^- (aq) → AgCl (s).