I see you have the Custom Design upgrade on karinkoolen.com, so the easiest way would be to create the rule in CSS and then all you would have to do is add the class designation to the blockquote. It can be done without CSS, but it requires you to write all the CSS inline in the post or page, each time you use it. I see you have some basic blockquote styling already, so add the following CSS to your custom CSS. I've provided a right pull quote, but you can use it as a guide and create a left as well and change the "float" to left. You can modify the width also, and you should also narrow and widen your browser window down to smartphone size to see how it will look on small devices.
In your post or page, you would then put in the blockquote as you normally would and then switch to the Text tab and add the class declaration to the opening blockquote tab like below.
<blockquote class="pull-right">Your quote text here.</blockquote>