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This reaction involves a base (NaOH) and an acid (HCl), so it's a neutralization reaction, which is a special type of double-displacement reaction. Follow this procedure to write balanced molecular equations for double displacement reactions, when you know only the formulas of the reactants:
The reason NaCl doesn't change the pH of a solution is because the cation (Na+) and anion (Cl-) that are produced when NaCl is dissolved are really weak acids and bases. We know this because their conjugate acid and base partners are really strong acids and bases. The conjugate base of Na+ is NaOH and the conjugate acid of Cl- is HCl. Look how tiny those dissociation constants are. Those dissociation constants tell us that the reaction will lie very far to the left.