Below is a snapshot of the relevant section from the IRS website showing your options.
The first big qualifier is your "dependency" status. IF your parents are claiming you as a "qualified" dependent on THEIR tax return this information will be relevant to you. IF you are "independent" and are NOT being claimed by someone else then this DOES NOT apply to you.
If you have more than $1,000 in "unearned income" then you must file a tax return. Unearned income would be interest on savings, Capital Gains on stocks, bonds or some other qualified investment. In short, it is money you get that is NOT from salary, wages, bonuses, tips, etc. If you are not sure about this part, check with a professional tax professional.
MOST young people fall into the second point below. The cut-off is $6,100. If you make even $1.00 over this you must file a tax return! Remember, the IRS already has copies of all your W-2 forms in their possession. They are just waiting for you to report what they already know.
If your Gross Income (total wages, salary, tips) is LESS than this amount then you are not required to file a tax return. HOWEVER (and this is a BIG however) if you had ANY Federal With-holding from your check(s) throughout the year you must file a return in order to receive a refund of the with-holding. The IRS WILL NOT hunt you down and remind you the US Treasury has some extra money for you!
Caveat: Regardless of how much you earn, especially if you are a college student receiving financial aid, it is good policy to file a return even if you don't have to. It helps to have that paper trail for filling out the FAFSA and other requests for aid.
If you know during the year that you will not earn at least $6,100 in GROSS earnings, you can amend your W-4 form that you fill out at work that tells your employer how much to take out of your paycheck for Federal With-holding. You can request to be EXEMPT from with-holding and no money will be with-held from your check because you do not believe you will owe any income tax. BE CAREFUL about this. Don't flirt with that $6,100 mark.
Here is a W-4 form with the line to do this highlighted in YELLOW. Go HERE to print your own out.
NOTE: I am not a tax attorney or qualified tax preparer. I just play one as a high school economics teacher. :)