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/ )
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.
The PMC Chair should take care of this when creating your account, but if they forgot, mail the email@example.com asking to get added to the OOZIE JIRA as committer.