First of all you need to get involved and contribute via the mail list, forums, edit the documention, work on the issue tracker and submit patches.
Once you're contributing and your work is good, the Oozie PMC may invite to become a committer by (after running a vote). When that happens, if you accept, the following process kicks in.
Note that becoming a committer is not just about submitting some patches; its also about helping out on the development, user issues, documentation, etc.
(Note for PMC chair: to create an account go to https://id.apache.org/acreq/pmc-chairs/ )
Once you've got your Apache account working you need to enable SVN access, refer to the Committers for details on how to use svnpasswd.
(Note for PMC chair: if the new committer does not have write access to Oozie SVN repository, login to people.apache.org an run modify_unix_group.pl oozie --add=<NEWCOMMITTERID>)
The committers list displayed in 'Project Information --> Team' page of the Oozie site is Oozie's site POM file. Refer to the How To Update Oozie site page for details on how to edit and publish the updated site.
Mail the email@example.com asking to get added to the OOZIE JIRA as committer.