If you want to integrate forums into your Joomla site, try Joomla Board
Once you have JoomlaBoard installed, you can go to Components -> Joomlaboard Forum to configure and administer the forum.
Go through the Joomlaboard Configuration.
Then set up your form in the Forum Administration. You need to set up a Category which is a container for your Forums. Posts can only be made to Forums and Forum must be within a Category. So you will need to have at least one Category and then one Forum under that category. Then publish all the Categories and Forums.
The User Administration is where you can view your users of your forums.
Now create a new menu with the selection of “Component”.
Joomla-SMF Forum Component by JoomlaHacks.com
If you want to use Joomla with Simple Machines forum instead, then you can use Joomla-SMF Forum Component by JoomlaHacks.com with is associated User Guide, Forum, and Help Topic. Joomla-SMF Component has optional modules to display recent posts on your front page.
What happened to Joomla-SMF Bridge?
Forum as a separate entity.
Alternatively, you can setup your forum totally separate from your website. And then skin the forum to match the site and integrate into it via a menu link. The method does not require you to hack Joomla code or use bridges and hence will make upgrade forums and data migration to different forums easier. But the drawback is that the author and publisher logins are totally separate from each other. Hence you might want to move the Joomla login component to separate page that only authors and publishers will know. That way, forum users will not try to use that login.
Adding a menu to your separate forum.
Go to the menu in the Admin console and click New menu. Then select Link URL as the menu type.