It's really not that easy unless the CMS tool your using is specifically built around the forum you want to add. If you're making the CMS, you should start with installing the forum and build your CMS around it IMO. AS IN, use the phpBB database to hold your site's user table containing PMs, post count, user, pass, email etc etc...
You probably have to brush up majorly on PHP and MySQL to accomplish this. You also have to take a month or two out of your life to learn phpBB, vBulletin, or whatever forum you wish to use and master.
If you truly dedicate yourself, maybe you'll create a tool that hasn't been perfected just yet
If you just want to have two sepperate databases (the forum and your site) with matching user lists, you can edit the forum's login script and make it register ppl to both databases, then do the same to your login scripts. You can, from here, either rely solely on the forum's register page to get your users, or make your own register page and disable the forum's. Or keep both.
Either way, the login+register pages+session variables all need to match up from forum->your site and back. You don't want people to have to login twice, and you most certainly don't want them to have to register twice. I've seen sites (and in my early days made some) that require 3-4 accounts, held sessions to some logins, not others, and even encourage using different information for different logins.
You don't want any of that bullshit. 