When I install it, I just follow their installation instructions (found in install.html). Boiled down, that is:
- Make the database and user (about 12 hours in advance).
- Upload everything to the server.
- Go to the installation page and enter all the data. (don't put http:// in front of your domain/server name!)
- Click Submit, wait for table creation to finish (I sometimes check the db at this point to make sure that it's done).
- Remove the leftover files (see Important Security blah blah section for details).
- Open the forum!
I haven't had any problems, but I also go through the mySQL user and db creation process about 12 hours before I'll be installing phpBB, just in case.
You haven't really given me details on exactly when this error is occuring - when you click Submit to set up the tables? when you enter phpBB for the first time? so this is the best I can do right now.
If you can give me more details, I can try to help you out more.