Separating into half reactions:
Oxidation half: Cu → Cu2+
Reduction half: NO-3 → NO2
Balancing oxygen and hydrogen atoms:
NO-3 + 2H+ → NO2 + H2O
Balancing charge by adding electrons and making the number of electrons equal in the two half reactions:
Cu → Cu2+ + 2e-
2NO-3 + 4H+ + 2e- → 2NO + 2H2O
Adding the two half reactions to achieve the overall reaction:
Cu + 2NO3 + 4H+→ Cu2+ + 2NO2 + 2H2O