The steps!
  • separate the reaction into "half-reactions"
    Cu → Cu2+                             NO3- → NO2
  • balance oxygen (use water) and hydrogen (use H+ for acidic solutions)
    Cu → Cu2+                           2 H+ + N
    O3- → NO2 + H2O
  • balance charges, using electrons
    Cu → Cu
    2+  + 2 e-             e- + 2 H+ + NO3- → NO2 + H2O
  • multiply half-reactions as needed to make electrons the same in both
    Cu → Cu2+  +
    2 e-             2(e- + 2 H+ + NO3- → NO2 + H2O)
  • finally, combine the half-reactions once more, simplifying where possible
    Cu + 4 H+ + 2 NO3- → Cu2+ + 2 NO2 + 2 H2O