To ensure your changes take effect by the next payroll, submit them by the 10th of each month for the monthly payroll. You may make changes to your W-4 and direct deposit up until the payroll is being run. As the date for this varies each month, you should refer to the Payroll Calendar  to determine the exact cut off. Be sure you make your changes at the same time your leave or time reporting must be done.
For the biweekly payroll cycle, complete your changes before your timesheet is due to your supervisor for approval.