expected unqualified id-before '/' token ------ can someone help, please
OK, you just had a couple of minor typos.

It's nice to break up your code for readability, but single-line comments comments start with a double slash //, rather than a single.

Also, you had mis-spelled 'delay' in your loop.



This should compile without errors:

/* Multiple State Handling
* 05-22-2019
*/

#define button 3                        //Push button on D3
#define lowbeam 5                       //Low Beam on D5
#define highbeam 6                      //High Beam on D6
#define gate 7                          //Gate on D7

//------------------------------------------------------------------------

int state = 0;                          //integer to hold current state
int old = 0;                            //integer to hold last state
int buttonPoll = 0;                     //integer to hold button state
//-------------------------------------------------------------------------

void setup() {
  pinMode(button,INPUT);                //button set as input
  pinMode(lowbeam,OUTPUT);              //relays set as outputs
  pinMode(highbeam,OUTPUT);
  pinMode(gate,OUTPUT);

  digitalWrite(lowbeam,LOW);            //initial state as off
  digitalWrite(highbeam,LOW);           //initial state as off
  digitalWrite(gate,LOW);               //initial state as off

}
//-------------------------------------------------------------------------
void loop() {

                                        //debouncing routine to read button
  buttonPoll = digitalRead(button);     //poll state of button
  if(buttonPoll == 1){                  //check if it has been pressed
    delay(50);                          //wait 50msec
    buttonPoll = digitalRead(button);   //poll button again
    if(buttonPoll == 0){                //if it is 0 consider 1 press
      state = old +1;                   //increase state by 1
    }}
  else{                                 //if button has not been pressed
  delay(100);                           //wait 100ms
  }
  switch (state) {                      //react to button press &amp; state
    case 1:                             //if state is 1
      digitalWrite(lowbeam,HIGH);       //lowbeam relay on
      digitalWrite(highbeam,LOW);       //highbeam relay off
      digitalWrite(gate,LOW);
      old = state;                      //set old state as current state
      break;
    case 2:
      digitalWrite(lowbeam,LOW);
      digitalWrite(highbeam,HIGH);
      digitalWrite(gate,LOW);
      old = state;
      break;
    case 3:
      digitalWrite(lowbeam,LOW);
      digitalWrite(highbeam,LOW);
      digitalWrite(gate,HIGH);
      old = state;
      break;
    default:                            //if state if no 1,2,3
      digitalWrite(lowbeam,LOW);        //all relays off
      digitalWrite(highbeam,LOW); 
      digitalWrite(gate,LOW);
      old = 0;                          //reset to all off/state 0
      break;
  }   
}