Ah, this shouldn't be too hard. I've done this before. First things first, you need to set up a working website. The method depends on whether you'd like to host it locally, on your own computer, or if you'd like to pay for better hosting. The other thing, regarding a domain: depends on if you want to pay for a good domain, or if you'd rather stick with a subdomain on some other commercial website. If you take that route, you'll have to look up how forwarding nameservers and such. Not too bad, it's just dealing with getting the domain of the site to work.
Secondly, you'd have to get a server up and running. If you're running Linux, I'd suggest LAMP for a first time. Windows, I think it's WAMP. What that is is Apache, MySQL, and PHP. Apache is the webserver. It's what runs on your computer to broadcast your webpage to the world once they connect to your computer. MySQL as I'm sure you know is the database. That's what stores all of your users and passwords and shizz. But if you were going to install phpBB, then it would create and handle it's own data in the database. You wouldn't really have to mess with it that much unless you were planning on tweaking, adding, or removing things from your site to make it more original. PHP is just a sexy language website devs like to use to make their site more sexy. Keep in mind that I'm sure you know a lot of this. I just don't want to miss anything, and this way other users viewing this will know exactly what to do. As for setting up the LAMP or WAMP or whatever, after you install it you should look up how to set it up. There are some things you're gonna have to go through and configure to make everything go the way you need it to.
After that, you need to install and set up phpBB. I've personally done this before as a test a few times. One time using godaddy's hosting services which are the shittiest shit I've ever seen. IMO. But if you're not into the whole managing your own box, you can always role with that and it'll be a lot easier than installing phpBB on a local box. Anyway, I'd say look up a good tutorial or something on installing and setting it up for your specific OS. Once again, configure it after that.
That's just a broad rundown tutorial.. I can almost guarantee you'll have more questions, so please feel free to post back with any questions or updates on your progress. It's a lot more complicated once you get into it, but while you're down in there troubleshooting all the bullshit you learn a hell of a lot.
For those about to hack, I salute you.