I live in NY but work in NJ. Both States took state income taxes. I have filed for the NJ, but could not find where to enter NY state income taxes that were taken as well. How do I do that?

You have to file NJ tax return for income earned while present in NJ. This will be nonresident tax return.
You will also file NY tax return reporting your worldwide income including NJ income. Also claim credit for taxes paid to NJ. Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)

Claiming a tax credit for taxes paid to another state is probably a bit beyond the skillset of the average taxpayer.

Further, to do so using tax software, it would require you buy the federal tax software and tax software for BOTH states, which could add up to a significant purchase price. Plus, there is no guarantee that you would prepare the returns correctly.

Given these facts, RUN, do not walk, to the nearest tax preparation office to get professional help.

OR you can contact me, since this IS what I do. If you want my professional help, double-click on my title above, then scroll down to the bottom of the page where my signature is located to get my email address. You will find my fees to be most favorable when compared to what tax preparers charge in New York and New Jersey.

I have filed for the NJ, but could not find where to enter NY state income taxes that were taken as well. How do I do that?

You don't - taxes you paid to your home state are immaterial to the state where you work. As a non-resident you pay tax to NJ only on the portion of income that is NJ-based. You complete the NJ return first. Then when you complete your NY return you will first calculate a total tax as if you have to pay tax on all your income, but then you take a credit on your NY return for taxes paid to NJ that reduces the amount you owe to NY.