If you operate your business as a C Corporation or an S Corporation you will be an employee of your corporation and your corporation will need to withhold income and employment taxes and pay them to the government. Your corporation must give you an IRS Form W-2 by January 31 each year and send a copy to the government by mid-February.
Tax may also be withheld from certain other income—including pensions, bonuses, commissions, and gambling winnings. These amounts will be shown on some version of IRS Form 1099. In each case, the amount withheld is paid to the IRS in your name.