creating table syntax error 1064
I see a few issues with your existing code to create the waiters table.

First, the index creation code is incorrect.  The column to be indexed should be inside the parentheses -- INDEX  (manager_id).

Second, you are trying to add an index on a column that is not listed in your waiters table. You need to include the manager_id as a column. 

Third, the syntax for the FOREIGN KEY constraint is incorrect. The syntax is from the MySQL docs is:

[CONSTRAINT [symbol]] FOREIGN KEY
    [index_name] (index_col_name, ...)
    REFERENCES tbl_name (index_col_name,...)
    [ON DELETE reference_option]
    [ON UPDATE reference_option]


So your code should be:

CREATE  TABLE `waiters` (
  `waiter_id` INT NOT NULL AUTO_INCREMENT ,
  `name` VARCHAR(45) NOT NULL ,
  `password` VARCHAR(45) NOT NULL ,
  `manager_id` INT NOT NULL,
  PRIMARY KEY (`waiter_id`) ,
  INDEX  (`manager_id`) ,
  CONSTRAINT FK_Manager
    FOREIGN KEY (`manager_id`)
    REFERENCES `managers` (manager_id)
    ON DELETE NO ACTION
    ON UPDATE NO ACTION)
ENGINE = InnoDB;


See SQL Fiddle with Demo