my employer requires us to work on saturdays without pay. say they will gives a day off during the year. is this legal?

Short Answer: NO An employer who is subject to the Fair Labor Standards Act (this is farily technical but if your employer has more than $300,000.00 in gross income per year it is highly highly liklely to be subject to that law), must pay its employees 1.5 times their regular hourly rate for hours worked over 40 in any work week.  A "workweek" is any 7 day period the employer elects.  Most employers run their workweek from 12:00 a.m. on Sunday to 11:59 pm on Saturday.  However it is permissible to run on other schedules, ie Wednesday to Tuesday. If the employee works more than 40 hours in the workweek, he must be paid for the overtime.  It is not legal (except in certain government employment) for the employer to give the employee an extra day off in a future workweek.  It is permissible for an employer to give an employee an extra day off during the same workweek.  Thus if an employee worked 10 hours a day Monday to Thursday and got Friday, Saturday and Sunday off, no overtime is due.