You can jump to new replies (and skip those you've already read) in two ways:
1. If you're viewing the list of threads in a forum, click the orange "View New" button immediately to the left of a thread title. Here's where to look for the button when you're viewing the list of threads (see the button circled in purple below):
This button is available on all threads with unread posts, so you can choose whether you want to view the entire thread (click the title) or just the unread posts (click the button).
2. If you're already in a thread, click the "View First Unread" link at the top left of an open thread.