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You need to be at least bilingual know English and another language really well. There are no formal graduate or post graduate qualification requirements. To work within Australia, you need accreditation or recognition from NAATI (National Accreditation Authority for Translators and Interpreters Ltd).  Some university courses and TAFE courses lead to NAATI accreditation or recognition and NAATI holds its own accreditation exams. 

The raw materials are language, general knowledge and cultural awareness. Vocabulary range is vital, and tertiary training will extend your vocabulary. Pronunciation and clarity of speech help, and since you are a background service provider, absence of self importance will help too. 

University qualifications in the humanities are excellent as general background training for interpreters. Interpreting is however intensely practical, not analytical, and therefore not well suited to academic training. You learn on the job - there is no other way. A degree in interpreting does however confer prestige, and practice in conference interpreting may only be available via a training course. TAFE has diploma courses. There are various university courses in interpreting. The University of Western Sydney has several at Bachelor of Arts and postgraduate level. Macquarie University has a postgraduate diploma, and the University of Queensland is known in particular for Japanese.

The field is fluid and courses do change. Check individual institutions for their offerings.

The entry criteria for tertiary institiutions differs from year to year. The above comments are a guide only. To gain specific entry criteria either contact the relevant university or use Hobson's The Good University Guide.