I always wanted to have a detail document before actually working on the task. Here is the detail step by step doc on applying 10.2.0.5.6 patch on 10.2.0.4 Linux 64 bit.
Update: 18/7/2012 : After applying 10.2.0.5.6 patch dbms_scheduler jobs were effected, jobs do not run at scheduled start time. For example there was a job to populate some rates, scheduled to run at 10:00 AM everyday, after upgrade it never ran at 10:00 AM. This effected other dbms_scheduler jobs which were dependent on this job. What caused this and how to fix it ? Refer my new post fix dbms_scheduler jobs after upgrade