Answer by Wray Rives:
First I suggest you or your employer contact a US tax professional, because there are a number of tax issues besides just the employment taxes and even the employment taxes could be a complex issue, depending on your employment relationship with your employer.
Now to answer the best I can without a lot more information, if you are truly an employee, working and residing in the US, then you will owe US federal income tax, US FICA and Medicare tax plus depending on which state you live in, you will owe state and possibly city level income tax. Your employer will need to withhold all of these taxes from your pay and remit them to the IRS and appropriate state tax authority. In addition, your employer will owe employer share of FICA and Medicare tax, plus state unemployment and federal unemployment taxes. Depending on what state and city you work in, there are other potential employer taxes that may be owed also.
Your employer will need to file federal and state employment tax returns quarterly to report those taxes. They will also be required to make electronic deposits for the federal and possibly the state and city level taxes or will at a minimum need to send a quarterly payment for the state and city taxes if any. Finally your employer will need to file a W2 form for you at year end to report your total earnings and taxes withheld.
Your employer should start by reading Circular Efrom the IRS.