Indonesia is a cultural country that consists five religions, Hindu, Muslim, Buddhist, Protestant and Catholic. A legally married in Indonesia could be done for those couple who are do one of those religions and must be in the same religion belief to one another.
First thing to do is obtaining CNI or Certificate of No Impediment to Marriage that is stating there is no objection for you to get married (some countries called it with different name, e.g Affidavit of Marriage Letter for British). For this, you must visit your Embassy or Consulate representative in Indonesia.
To be a legally married, the marriage will be registered with the district Civil Registry and the ceremony must be performed under religious rites. But specially for Moslem marriage, it does not require approval from Civil Registry except for a few countries that require residents to include a certificate from the registry office.
Please note that a Catholic couples need to be married in a Catholic Church. But they still may have a Christian Wedding out of the Catholic Church (e.g Chapel, beach, villa, etc) after they make statement that they agree to be married as Protestants. And also a divorced people can not remarry in the Catholic Church.
Additional fee will be required for residents that need to re-register the documents in their country, happening with some nationality which has really strict rule e.g Netherlands.