The reaction is called neutralization. Both acid and base dissociate. The H+ of acid and OH- of base associate to be H2O, canceling the acidity and alkalinity of acid and base respectively.
The exact reaction depends on the specific acid and metal, but usually an acid will react with a metal to produce a corresponding salt and hydrogen gas.
While neutralization is what happens, there is also these formulae that can go with it. A word equation is: Acid + Base > Metal Salt + Waterand a chemically balanced equation is: HCl + NaOH >...