How to set up multiple fields as primary key in MySQL?
Use a compound primary key:

CREATE TABLE yourtable 
  ( 
     employeeid  INT, 
     blahblah    VARCHAR(255), 
     blahblah2   VARCHAR(255), 
     recordmonth DATE, 
     recordyear DATE, 
     PRIMARY KEY (employeeid, recordmonth, recordyear) 
  ) 


And if your table already exists, drop the old primary key:

ALTER TABLE yourtable
DROP PRIMARY KEY;


And recreate it:       

ALTER TABLE yourtable
ADD PRIMARY KEY (employeeid, recordmonth, recordyear);