I work in CA but am a resident of NY. My employer withheld NY taxes (reported in boxes 15 and 16 of my W2). However, no taxes were withheld for CA even though CA and NY do not have a reciprocity agreement. Is it correct that I still need to file in both CA and NY? Should the W2 show California wages as $0, but wages should be reported on my California return?
Yes, you will still need to file both NY and CA.
In general, your home state will tax all in come from all sources. What you will do is you will file a nonresident return for the states that you do not reside in, but you visit for work and earn money in. When you file, you will fille out your nonresident states first. Then you will fill out your resident state, claiming a credit for taxes paid to the nonresident states on your home state return. You may or may not still end up owing money to your resident state depending on whether or not their tax rate is higher or lower than your nonresident state. If the non resident state had a higher tax rate than your resident state, your credit will be limited to the amount of tax you would have paid to your resident state. They will not give you a refund of the taxes you paid to the nonresident state.
To add a bit to @Vanessa A 's answer:
California can tax you as a non-resident on any income you have from work you actually (physically) perform within California. If you have such income, you report it by filing a non-resident California tax return.
Your resident state of New York can tax all your income, regardless of where you earn it. NY will give you an "other state credit" for the taxes you pay to a non-resident state, so as to avoid double taxation. You claim that credit on your NY tax return.
If you have income taxed by two states, then in TurboTax (with a couple of exceptions), you must complete the non-resident state return first, before you do the home state return, so that the program can calculate and apply the other-state credit.