How does one create a RMAN recovery catalog?

Start by creating a database schema (usually called rman). Assign an appropriate tablespace to it and grant it the recovery_catalog_owner role.

Look at this example:

sqlplus sys
SQL> create user rman identified by rman;
SQL> alter user rman default tablespace tools temporary tablespace temp;
SQL> alter user rman quota unlimited on tools;
SQL> grant connect, resource, recovery_catalog_owner to rman;
SQL> exit;

Next, log in to rman and create the catalog schema. Prior to Oracle 8i this was done by running the catrman.sql script.

rman catalog rman/rman
RMAN> create catalog tablespace tools;
RMAN> exit;

You can now continue by registering your databases in the catalog. Look at this example:

rman catalog rman/rman target backdba/backdba
RMAN> register database;

One can also use the "upgrade catalog;" command to upgrade to a new RMAN release, or the "drop catalog;" command to remove an RMAN catalog. These commands need to be entered twice to confirm the operation.