I am a foreign student who study in US with F-1 visa, and I worked with my university from August 2009. So, I should be a full year non-resident or part-year resident for 2009?

On F1/OPT you are exempt from residency for 5-years. You must file non-resident tax return Form 1040NR or 1040NR-EZ and Form 8843. Your income is not subject to FICA taxes but you must pay federal and state income taxes.

On your income you will get deduction based on tax treaty between the U.S. and your country. Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents