You should call the IRS to ask how to find out if you are a contract worker (self employed) or an employee. I can't tell you without knowing specifics about what you do, but I suspect that you are working for a tax cheat and a law-breaker. I see this a lot. Small companies try to get out of paying their share of the Social Security and Medicare taxes, which are the same amount that you pay. They are supposed to withhold your share from your pay, match it, and send it to Social Security. They are also supposed to withhold state and federal income tax and send that to the IRS and the state tax revenue office.
So you need to find out if the law has been broken and you have been cheated.
If not, if you really ARE an independent contractor, your income will be reported on a 1099, not a W-2. This means that you are self-employed.
If you can claim yourself as a dependent, you won't owe any income tax if you earn less than $10,000. However, you still MUST file.
This is because you WILL owe the self-employment tax. This tax is both shares of Social Security and Medicare taxes, and you begin to owe as soon as your income reaches $400. If you earned $10k and had zero allowable business expense deductions, you would owe roughly $732 in self employment tax. You calculate it on Schedule SE and report the result on Form 1040.