Check out this tutorial: http://jshamsul.com/2012/02/08/wordpress-get-first-paragraph-from-post/
There the author puts all the paragraphs into array. So you could possibly pull out the first, second, thrid… paragraphs from that array.
As for smashingmagazine.com styling the first paragraph. They do it with CSS :first-child pseudo-class like this:
p:first-child {
/* your styles */
}
More info about :first-child – https://developer.mozilla.org/en-US/docs/CSS/:first-child
You could also style the second paragraph with :nth-child like this:
p:nth-child(2) {
/* your styles */
}
More info about :nth-child – https://developer.mozilla.org/en-US/docs/CSS/:nth-child