In our old forum platform, you could do a search for new posts since your last visit. In this platform, there is no direct equivalent to that but you may not need it.
The list of topics that you see on the home page is sorted by the last post date. The most recent topics are at the top of the list. New posts (that are unread for you) will be flagged with the NEW flag. Those topics with unread posts will have a "First Unread Post" link that will take you straight to the first unread post for you within the topic.
Enjoy the Community. We're glad that you're here.