I was wondering the same in a post earlier today. Things have seemed quiet since joining the new site, either because of the holidays or because people are still figuring out how best to use the system.
Some of the old forums have been created on this site as groups. The best way to get easy access to the group forums is to join the corresponding groups. That way the groups show up on the right hand side of your home page, with a forum link under each one. All you have to do, is click that link. Also, if you join a group you can also post to its forum.
The other way to get to the forums is a little more cumbersome, but doesn't require you to join. Go to the menu at the top of the screen called Groups, click on it and select All Groups to see a list of all groups (there are four pages worth so far). Find a group you might be interested in, click on it, and click the Forums tab to take you where you want to go. I'm afraid you have to repeat this step for each group you're interested in. That's why I find joining groups is the easier workflow. You can, however, read the content of most groups without joining. Some are made explicitly private by the creator/moderator for their own reasons.
I've also read that Sol is going to resurrect some form of the old groups on the new site. I'm not sure how he'll pull that off without further complicating the group forum concept already in place. Will that mean there will be two places to go to post/read? Not sure yet, and it will probably take some time, although he is very responsive.
As a workaround for the old forums, Linda Lee created a group here called Old Forums, with one thread for each of the old forums (e.g., shred thread, strongest start, member announcements, etc.). Unfortunately, with only one discussion thread for each of the old forums, you really can't have multiple separate conversations going on in the same thread (e.g., discussions about two different pieces of work being shredded, or multiple conversations about writing tips & advice, and so on).
Since we're allowed to be a member of ten groups at a time, joining the groups of interest to you is probably the best bet. Have a look through all of the available groups so far and join those you like, or create new ones. You can announce any new groups you created here in the Premium forum. If there are particular people you want to explicitly invite into a group, make a connection with them and then send them a private message.
Hope that helps.
Dirk