In a previous post, I demonstrated how to center align your WordPress blockquote, if you are looking for some additional styling, take a look at this custom CSS:

blockquote {
max-width: 500px;
text-align: center;
margin: 15px;
padding: 15px;
font-family: Helvetica Neue,Helvetica,sans-serif;
font-size: 22px;
color: #95a5a6;
background: #ccc;
}