Since you are working as an independent contractor, the person or business that is paying you is not your employer. They are your client.
Since no income tax is withheld from the payments that you get, you will have to make quarterly estimated tax payments. Be sure to read How Do I Make My Quarterly Payments? (on the IRS page that VolvoGirl referred you to), and also Estimated Taxes on the IRS web site. If you live or work in a state that has state income tax, you will also have to make quarterly estimated tax payments to the state.
