Hi Jimmy,
You should be able to simply use Postgres's standard tools for importing the database onto the new server (or perhaps even just copy all the underlying files).
Once you have the old version's database on the new server, and you have the new version of Review Board installed, you'll need to make sure you copy the site directory from the old server to the new one and then edit the site directory's conf/settings_local.py file to point to the new database.
It's important that you do copy the site directory over, as it contains the file attachments, some data files, and the key used for encryption for that install.
Then, you just run `rb-site upgrade /path/to/sitedir` to have Review Board upgrade the database schema from the old version to the new one.
Christian