You will put the entire amount of the income that was earned in New York state. You enter the amount, not the percentage.
You can see the amount that your employer reported for NY State earnings in Box 16 on your W-2 form. That is the amount that you use to attribute wages earned in the state.
You won't need to worry about paying income tax in multiple states, even if you have to file more than one return. When you live in one state and work in another, the state where you work usually gets to tax you and will withhold the appropriate amount from your paycheck each week.
