Let's cover the technicalities of terminology first, so we're both on the same page. If you are an independent contractor then the person or entity that pays you in that capacity is your client - not your employer per-se. Any and all income earned by you as an independent contractor is considered self-employment income that earned while "in business" for yourself. Those who pay you as an independent contractor are not required to withhold taxes for any taxing authority at all. But they can if they so desire. Either way, you are the one responsible and required to pay taxes on that income to the IRS, and if your state taxes personal income you have to pay taxes on that income to your state too.
Generally, you pay taxes on self-employment income each quarter.
Now, for all self-employment income weather it's reported on a 1099-MISC or not, you will report that under the Business tab in the Business Income & Expenses (SCH C) section of the program.
