When using MS SQL Server as the IDM database, we have used the "Log Shipping" functionality to replicate the DB data to the DR database.
Similar to what Gil mentions, this DB is in offline mode and all applications are in the shut-down state. In the case of IM, the DR app servers are not in the same app server cluster as the primary app servers.
In the case of a disaster, the DB is brought online and the applications are started up.
We hat a MRPO of 15 minutes, so logs were shipped every 15 minutes.
I'm not so familiar with the Oracle tools, but I believe that there are native and 3rd-party options for this.
As KennyV says, we used aliases in the hosts file so that prod and DR applications can use the same alias name to point to their respective databases
We used asynchronous replication to replicate the user store and provisioning directory to the DR site.