First, you will need to grab a copy of your old database. The file is usually called pwman.db and is stored in the /home/username/.pwman/ directory.
If you can't find it there, take a look at your /home/username/.pwman/config/ file, and it will tell you where the file is.
Copy the db, and move it to a safe location.
Install pwman3 on your new server by following the new installation instructions. You can take a look back at this page, or look at the content below.
Using a fairly modern version of Ubuntu/Debian (tested on Ubuntu 8.04 LTS 64bit) you can throw this command in the terminal:
sudo apt-get install pwman3
Run pwman3 be typing pwman3 at the command line.
I suggest configuring the same master password as you had in the previous version1)
Take your backed up copy of pwman.db and copy it into your new /home/username/.pwman/.