I don't understand.

You are probably not doing the reaction in vacuum

would you include oxygen from the atmosphere in that equation?
and if it's in water, would that be included in the equation?

Hm.. I haven't seen any reaction like this one before, that is where ammonia is oxidised to nitrogen gas from copper chloride... And that HCl is formed, which is supposed to react to ammonia to form ammonium chloride...

But if that indeed takes place, I would place my bet on water, water coming from CuCl2 (aq), because [Cu(NH3)4(H2O)2]^2+ is a complex which is responsible for the deep blue color of copper + ammonia solutions.

But how would you get water from CuCl2?

CuCl2 is aqueous, hence, it's in solution, and when solution is mentioned, water is present :)

How would you incorporate water into the reaction? Would you put it in with the reactants? How would you balance the equation?

You can incorporate it with the reactants [ + H2O (l) ] and balance accordingly.