How do I tell how much I was double taxed?

Prepare the NON-resident state return first---that would be NY.    Then prepare your NJ state return.

My question is more so where am I getting these numbers from? It doesn't explain.

If you do the NY return first and then the NJ return a lot of those numbers will be populated for you.  Since you already started the New Jersey return first you need to delete all of the state returns that you have done so far and start over.