The conversion of a phpBB2 forum to phpBB3 is relatively easy.
Please bear in mind that the conversion will bring over only the registered users and posts.
If you are installing phpBB3 manually all you need to do is click on the Convert tab once the installation is completed.
The conversion should be performed by accessing the install directory via your web browser. Depending on where exactly phpBB3 is installed the URL will be similar to:
In the conversion area you should click on Convert:
At this point the conversion from phpBB2 is the only available option.
On the next page you will have to enter the required details for your old phpbb2 installation. The database details can be found in the config.php file for the old forum. The path to the forum should be relative to the new location where phpbb3 is installed. Once you have supplied the correct details click on the Begin Conversion button. Here is a sample page with the filled details:
The conversion will process automatically. It will not make any changes to your old forum.
Upon completion it is possible for the script to request from you to rebuild the search index for the newly installed forum. You will be able to do this from the administrator backend.
At this point you should delete the install folder as you will no longer need it.
After performing those steps the conversion from phpBB2 to phpBB3 will be completed.