Should I file for exempt if I didn't do taxes last year and expect to earn less than $10000 this year? I am a dependent and a full time student

Students are not exempt from paying tax, so no, you do not say you are exempt.   Claiming to be "exempt" when you are not can cause problems for you.   If you are a W-2 employee, the employer will withhold Social Security and Medicare from your wages.   If your gross income is less than the standard deduction amount, you will not have federal tax liability, so very little will be withheld from your pay for ordinary federal tax.   You do not say what state you are in; depending on your state you could have a state tax liability.

Use the W-4 tool to prepare a W-4 for your employer.

https://turbotax.intuit.com/tax-tools/calculators/w4/ 

https://www.irs.gov/individuals/tax-withholding-estimator

https://www.irs.gov/pub/irs-pdf/fw4.pdf