Step 1: Write the skeletal equation of all reactants and products of the reaction.
Cu + NO-3 → NO2 + Cu2+
Step 2: Indicate the oxidation number of each element above its symbol.

Step 3: Identify the elements which undergo change oxidation number.

Oxidation number of copper has increased from 0 to +2 and nitrogen has decreased from+ 5 to + 4.
Step 4: Calculate the increase or decrease in oxidation number per atom. If more than one atom of the same element is involved, find out the total number of increase or decrease in oxidation number.

Step 5: Equate the increase in oxidation number with decrease in oxidation number on reactant side by multiplying the formula of oxidising and reducing agent. Multiply NO3- by 2 and Cu by 1.
CU + 2NO3- → NO2 + CU2+
Step 6: Balance all other atoms except H and O.
CU + 2NO3- → 2NO2 + CU2+
Step 7: Finally balance H and O by adding H2O molecule using hit and trial method.
- If reaction is taking place in acidic medium, add H+ ions to the side deficit in hydrogen atoms.
- If reaction is taking place in basic medium, add H2O molecules to the side deficient in hydrogen atoms and simultaneously add equal number of OH- ions on the other side of the equation.
Cu + 2NO-3 + 4H+ → 2NO2 + Cu2+ + 2H2O