if you try to use phpBB in an ISP's free web space. phpBB needs a database server, and php installed - neither of which will be the case in free space.
The following database servers are supported in phpBB:
1. MySQL 3.2x
2. PostgreSQL 7.x
3. Microsoft SQL Server 7/2000
4. Microsoft Access (via ODBC)
with MySQL being the most commonly used. I suggest that if you want to use phpBB (which is an excellent choice by the way) you'll need to forget your free space and sign up with a 'proper' web host. Good hosts will set you up with your own domain name, and will certainly have a package that contains everything you need to get your forum up and running.
FTP applications are readily available, and I recommend that if you are new to that technology you start with a good one - WSFTP Pro is my personal favourite.
Once you have all that in place you'll find that installing phpBB is pretty straightforward - the readme doc that comes with the software tells all.