Good afternoon all.
I recently took a job as a manager at a fast/casual dining restaurant. I am being paid salary, and when I took the job it was a 5 day work week, with 8 or 9 hour days expected of me. Since then, the owners have approached me asking me to work a 6th day with an increase in pay. My question is, by law, do they have to pay me overtime for working that 6th day? I have no problems working 6 days a wekk, but I want to be sure I am being compensated appropriately for my time.

It is likely, as the restaurant manager, and if your salary is at least $455/wk (that is the federal minimum, your state may have a higher one) that you are exempt from the minimum wage and overtime provisions of the federal Fair Labor Standards Act. It that case, the employer would not legally be obligated to pay you any more than your weekly salary ever, no matter how many hours you work.

You can go to http://www.dol.gov and drill down to the fact sheets about the Executive (and, possibly, Administrative) exemption criteria to compare your job duties and see if you qualify as exempt.