You should work on the NY return first inside of Turbo Tax. That helps the information from your NY return flow to the NJ return and the credit for taxes paid to NY. You wouldn't have to find the information yourself.
Your double taxed income is likely your NYS wages on the W2. However, it could be less if you have certain income adjustments such as an IRA contribution.
The figure comes from the IT-203, line 31. Your tax paid to NY on double taxed income is from IT-203, line 50.
Your tax paid represents the amount you actually owed to NY. So, if you had $3000 in NY taxes withheld and get a $500 refund, your tax paid to NY is $2500.
If you edit the NY return and go through it again, and then go back to NJ, these fields should populate.