To follow someone on the new QuitNet, just click their picture to access their profile page. Once there, you can click the "Follow" button in the top-righthand corner of the page. The member(s) you follow will be added to your "Following" list, and you'll see their activity when you use the Friends filter in the activity stream on your QuitNet homepage.
To unfollow someone, just go back to their profile page and click the "Unfollow" button. You can see a list of QuitNet members you are following by visiting your own profile page.