Processing is just a programming language. If you need to fire up a browser inside a Processing application, you'll have to stop using Processing as a language on its own, and simply use it as an API library inside a full blown Java application. It doesn't come with anything that acts as a browser, all Processing itself can do is link you out to somewhere (using the link() function call).
If you are running the sketch as an Applet, be aware this is no longer recommended; if you still have Java enabled in your browser, you've not been paying attention to the security news around Java the last few months. The general idea is that if you need a browser tie-in, see if you can make that work by using Processing.js (which runs Processing sketches in the browser by interpreting them as JavaScript, rather than by compiling them to Java VM bytecode and running that in a JVM). If you have lots of imports, this will not work, and you may have to go the plain Java route instead.