Incomplete info
where u have hosted the forum
if on a free host then ask the admins or the support for database backup
Most of the time on free forums u r charge a fee for backup

Then again u dint tel where u want to host the forum
its not possible to import database on free forums
u've to host forum urself with php and MYSQL enabled host

Upload the forum files after downloading latest phpBB to ur host
Install the forum
import the database through phpmyadmin
link it to the forum
and ur forum will be up again

Mind u that the phpBB without mods is rather useless
u've to apply some good mods to make it working