You're going to want to use jQuery's change event. I am displaying the text of your option as an alert, but you can display whatever you want based on your needs. (You can also, obviously, put it inside another part of the page...it doesn't need to be an alert.)

$('#myOptions').change(function() {
    var val = $("#myOptions option:selected").text();
    alert(val);
});

Also, note, that I added an ID to your select tag so that you can more easily handle events to it (I called it myOptions).

Example: http://jsfiddle.net/S9WQv/

As specified by JasCav using jQuery you can accomplish the same in javascript using

 <select onchange="alert(this.options[this.selectedIndex].text);">
      <option value='option1'>Gateway 1</option>
      <option value='option2'>Gateway 2</option>
      <option value='option3'>Gateway 3</option>
 </select>

Alternatively, onclick event of option, but note that it is not compatible on all browsers.

<select>
      <option value='option1' onclick="alert(this.value);" >Gateway 1</option>
      <option value='option2'>Gateway 2</option>
      <option value='option3'>Gateway 3</option>
</select>

You can write it as below mention using javascript.

document.getElementById("select").addEventListener('change', (event) => {
  console.log(event.target.value)
});

<select id="select">
      <option value='option1'>Gateway 1</option>
      <option value='option2'>Gateway 2</option>
      <option value='option3'>Gateway 3</option>
 </select>