In general:
If you are a resident of state A, you owe income tax to state A on all your world-wide income. If you physically work or live temporarily in state B, then you only owe income tax in state B on a non-resident tax return, only on income earned while living or working in state B--not where the clients are, but where you are physically located when you perform the work. State A will give you an offsetting credit for out of state taxes you owe.
However, New York applies a "convenience of the employer" test. If you work for a New York employer but live elsewhere because your employer wants to you (convenience of your employer), then your income is not New York income. If you work out of state for your own convenience, then your income is considered New York State income.
But, there is a special exception. New York can't tax you if you never (in the tax year) live or work in New York State. If you never set foot in New York State, then your income is not NY income, it is only CA income, and the employer should only withhold CA income tax. If you live or work in NY state for even one day (such as for a required annual training, meeting with supervisors, etc.) then all your income for that company is considered New York State income.
If your wages are considered New York income, then you will file a New York non-resident income tax return to report your wages and pay tax. Then, you will file a CA resident return to report and pay tax on all your worldwide income, including the NY wages, and you can claim an offsetting credit for taxes paid in NY. Since NY income tax for most people maxes out at 7%, and CA is closer to 10%, the credit will only partially offset your CA tax and you will owe some additional money to CA.
If your wages are not considered NY income, but you have NY withholding, contact your employer to change that. You would still have to file a NY non-resident tax return, but report zero NY wages (even if the W-2 says you have NY wages). You won't owe tax and will get a full refund of the withholding. Then you file a CA income tax return and pay taxes on all your income. Be prepared for NY to question whether you have NY wages under the convenience of the employer rule (by having proof that you are working in CA for your employer's convenience, or that you are working in CA for your own convenience but never set foot in NY during the tax year.)
