I am a salesman for a Bahamas based domain name registrar and hosting company.
I work out of NY from my home and am a US citizen.
How do I report my income to the IRS?
The company I work for does not have any other employee in the US (it's very small, including other 10 people from India and Panama).
They do not issue any W-9 or other tax documents...
It sounds like they are treating you as an independent contractor and simply paying you a commission. If so you are running your own business and need to pay your federal, state and city income tax just like any other business. The fact that the firm paying you is in the Bahamas really makes no difference; you are in New York, not the Bahamas, and thus pay US taxes.
If you are not an independent contractor but rather an employee, then they are doing business in the US (they have an employee, you, in the US) and they will be subject to US taxes and filing requirements. In this case they will need to comply with all the US requirements on employers such as unemployment insurance, workmen's compensation, FICA and income tax withholding. They will also need to issue a w2 form at the end of the year.
What do your check stubs say? Has the company been withholding your US taxes? Do they have your SSN? Do you have a contract with them? Did you fill out the W2 form? If you didn't do these things and no taxes have been withheld then you are going to need to declare that income on your taxes and you will be treated as an independent contractor.
If this is the case I hope you have set aside part of your income to pay these taxes, also, if you are going to continue with this company in this way then I believe that you can pay estimated quarterly taxes. This will be easier to do and has to potential to keep you out of trouble with the IRS by not waiting till the end of the year and potentially spending the money set aside for your taxes.
Tim - VA