RE:How to Build Up a Portfolio?
If you want to be a professional writer, there's no better way to prove your professionalism than by submitting your work to an editor. So understand that there's no avoiding that process, though writing for the school paper is always a place to start.
That said, starting a blog is a very good way to both practice your writing, find your voice, and, often, find an audience. Visit www.wordpress.com for tips on getting started, and set up your blog site for free.
Best of luck!