Edit in JSFiddle

function getRandomLetter() {
  var rand26 = Math.floor( Math.random() * 26 );
  return ( ( 10 + rand26 ) / 36 ).toString(36).substring(2);
}

$( function() {

  var $letterOutput = $('#letter-output');
  
  $('#get-button').click( function() {
    $letterOutput.text( getRandomLetter() );
  });

});