On bog standard iron, this is a fairly simple procedure. Download the patch, stop the databases and listeners and opatch the ORACLE_HOME. See general procedure Applying patches
a word about the different patching terminology;overlay, merge, bundle etc..

• how to apply patch in oracle

$ORACLE_HOME/OPatch/opatch lsinventory

$ORACLE_HOME/OPatch/opatch lspatches

dba_registry_history is a view on registry$history

col action_time for a21
col action      for a15
col namespace   for a15
col version     for a15
col comments    for a80 wrap
select action_time, action, namespace, version, id, comments from dba_registry_history order by 1;

Reference: Datapatch User Guide (Doc ID 2680521.1)

• Patching is now no longer performed inline. It is always done in a new ORACLE_HOME. So the databases do not need to be stopped until each one is moved to the new home.
• When the database is restarted in the new home, $ORACLE_HOME/OPatch/datapatch must be run to apply the SQL fixes.

select extract(sys.dbms_qpatch.get_opatch_list,'//patchDescription|//appliedDate|//patchID') from dual;

Now things are getting more interesting…

• Patching Oracle Database Appliance (ODA)
• Patching Exadata