By filling out the W-4 you are estimating how much tax you will pay at the end of the year, and they withhold a prorated amount out of each paycheck. The trouble is if you fill out the W-4 "correctly" will not correctly figure your taxes. You will almost always get a large refund or owe a large amount. For low wage earners, the W-4 almost always withholds too much tax, for high wage earners or dual incomes it almost always withholds too little.
If you put Single or Married and 2 exemptions the withholding is correct at zero. Social security and Medicare is simply a percentage of your income so there will always be money withheld for those categories.
More than likely you will receive a refund at the end of the year. With the earned income tax credit low wage earners often receive a "tax refund" in excess of any amount they paid in making it an entitlement program.
One way to be assured of this is filling out last years 1040EZ (if you have nothing but standard deductions) or this years 1040ES with your expected income for this year and the expected withholding. You can then adjust your exemptions accordingly to get as close as possible to zero.
For full disclosure high wage earning couples who fill out their W-4s accurately will owe the IRS in the tens of thousands of dollars because the withholding will be so inaccurate. To further exasperate this they will often have to pay a penalty for owing too much. Crazy huh? Follow the instructions on an IRS form accurately, and you will be penalized. These couples should almost always file M-0, and do additional withholding (line 6) to avoid the penalty.