If you're doing this for a client, I think you should get some assistance to make sure it goes well.
The database lives on a host that the client is (probably) paying for right now, maybe his web host. They probably have a control panel and in there some sort of tool for managing a database. Depending on the tool, there should be a way to export or dump the database. Once you have that file saved locally on your computer, you can go about using a similar tool on your host, in reverse though, for import instead of export. That takes care of the database.
Then you need to grab all the bbPress files off their web host, and transfer those to your web host.
If you're not changing domain names, just hosting, then you need only worry about DNS, not modifying any of the settings for the site (other than database connection details: those will certainly be different on your server.)
Also, in general, don't forget about any email addresses they might have created at the old web host. You'll need to recreate those on your server. That's got nothing to do with bbPress, but I almost always forget to do that, and then remember it later.
Good luck.
