I know how to balance a chemical equation but I am not quite sure how to find the product. My teacher is giving a final exam and I need to know this. Thank you.

You should know your general chemical reactions for this and a little of predicting if you come across a new type of reaction. First you should know these 'general chemical reactions' such as action of acid on metals, metal oxides, metal carbonates, on alkalis.
Then there are others such as displacement, reaction of water with alkali metals and alkali earth metals.

For instance, you should therefore know that:
Acid + Metal ---> Metal salt + Hydrogen gas
Acid + Metal oxide ---> Metal salt + Water
Acid + Metal carbonate ---> Metal Salt + Water + Carbon dioxide
Acid + Alkali ---> Metal salt + Water
Water + (alkali and alkali earth) Metal ---> Metal hydroxide (which is a base or alkali)

You should also know the reactivity series for certain reactions, namely displacement and other reactions which will come in higher classes.

For more specific info, ask!