So I am a student and will be making less than 6 thousand dollars this year, and so I'll be exempt from taxes. Can I use some of the money I make to contribute to a Roth IRA?
If by exempt, you're just referring to the fact that the income is less than your standard deduction and personal exemption, then yes, that money can be used to fund a Roth. Great time to do it.
To be clear, in 2014 the limit for an under 50 year old, is $5500 ($6500 if 50 or older). Only earned income may be used for deposits. No interest, dividends, etc.