To download the source of a site, it's easy, just use loadStrings and pass it the URL of interest:
Code:

String[] myStr = loadStrings("http://www.google.com");

// Make sure this works
for (int i=0; i<myStr.length; ++i) {
  println(myStr[i]);
}
 

To do the rest, your best bet is to read up on regular expressions and use the match function (see http://processing.org/reference/match_.html for docs on that).  I know this is a bit of a pain if you're not comfortable with regular expressions, but it's probably going to save you a lot of hassle over the alternative (which is, I suppose, using split - http://processing.org/reference/split_.html, though that will get nasty...).

You might want to collapse all the elements in the myStr array into a single string first, too, so that you can search the whole file at once instead of looping line by line (which will also be troublesome for you if html is split across lines).