1. Find your income exemptions
2. Find your pretax deductions, including 401K, flexible account contributions ...
3. Find your gross income
4. Check the state tax rate and the rules to calculate state income tax
5. Calculate your state income tax step by step
6. If you want to automate payroll tax calculations, you can download in-house ezPaycheck payroll software, which can calculate federal tax, state tax, Medicare tax, Social Security Tax and other taxes for you automatically. You can try it free for 30 days, with no obligation and no credt card needed.
You can also find guide on how to calculate state income tax automatically here.
Seven U.S. states currently don't have an income tax: Alaska, Florida, Nevada, South Dakota, Texas, Washington and Wyoming.