Fade out and change HTML, then fade back in.

anim.js

var $content = $('.content');
var $container = $('.container');
var quotes = [ /* array of quotes */ ];

var randomQuote = function(){
  return quotes[Math.floor(Math.random() * quotes.length)];
};
var changeQuote = function(){
  $content.fadeOut('slow', function(){
    $container.html(randomQuote());
    $content.fadeIn('slow');
  });
};