How do you balance copper II nitrate to copper II oxide, nitrogen gas and O2 gas?

1. Start with getting the chemical formula of the products.

Copper(II) nitrate: Cu(NO3)2
Copper(II) oxide: CuO
Nitrogen gas: N2
Oxygen gas: O2

2. Create an equation with the reactants on the left and the products on the right:

Cu(NO_3)_2 \rightarrow CuO + N_2 + O_2

3. Balance the metals (primary reactants) first. Move down to other reactants putting oxygen and/or hydrogen (if present) last. In this case, Nitrogen then oxygen

Cu(NO_3)_2 \rightarrow CuO + N_2 + \frac 52 O_2

4. If you don't like the fraction (it's not really an error), multiply everything to get it out

2Cu(NO_3)_2 \rightarrow 2CuO + 2N_2 + 5 O_2