It can be surprising, but you are correct (and so is the software
): Debian does not auto-upgrade your database clusters. It's all explained, please see:
$ zless /usr/share/doc/postgresql-9.0/README.Debian.gz
in short, you need to do:
$ sudo -u postgres -s
$ pg_dropcluster 9.0 main --stop
$ pg_upgradecluster 8.4 main
Now, double check that the new cluster is working correctly before removing the old one!
$ pg_dropcluster 8.4 main
If you have other clusters, you need to upgrade them manually. Check with:
$ pg_lsclusters
You also need to manually remove postgres-8.4 when all databases are upgraded.
edit: what you are "supposed" to do is up to you: postgres-8.4 is the default in Squeeze, so it will probably be supported for another 4 years. You can choose to stick with 8.4, or migrate to 9.0. You can also keep current databases on 8.4, and create new databases on 9.0. But if you keep the default setup (i.e. the "main" cluster on both versions), you *will* have to rename/delete one of them when you decide to upgrade the 8.4 cluster.