How to propely perform a recovery?
It could be a "cold backup" where someone shuts down the database and copies the PGDATA directory files.  If that is the case, it should be a valid backup.  You can test it by copying the entire directory to some test machine with the same architecture as the database server, taking that test machine off the network (in case it tries to reach out and touch someone when you start it up), and then start it up.  You can also run the program pg_controldata against this directory.  If the database was shutdown at the time the backup was taken, you will get a line like this:

Database cluster state:               shut down


This suggest it was a cold backup and should be valid, but it is not conclusive proof.

It could be a correctly taken hot-backup.  If this is the case, the directory should have a file named backup_label.  But again, this is not conclusive that the backup is complete and was correctly taken.  You need to test the backup.  The hot backup could be entirely self-contained, all the needed WAL being located in pg_xlog.  Or, it could be usable only in conjunction with an external WAL archive.

Finally, it could be that someone ran cp -r or similar against the database when it was in service without going through the proper steps, and created a useless backup.

You should be able to look at the backup script to at least see what it is attempting to do, that should be easier than doing a from-scratch forensic inspection of the back up directory.