Since there are no withholdings on 1099 income, you will need to adjust the W-4 with your employer to account for the extra income which can be done in section 2. If the 1099 consulting work is your only income I would recommend making quarterly payments based on your income to both fed and state. You can do this going to the state website and make a tax payment (where/what to click depends on the state).
Federal - https://www.irs.gov/businesses/small-businesses-self-employed/estimated-taxes
You can also use the Turbo Tax W-4 tool to estimate your tax liability and determine what tax bracket you are in.
This will help you determine how much you should pay in estimated payments each quarter.
