Australia
Most courses look at three things: your English test score (such as IELTS, PTE or TOEFL), your previous academic results, and any course-specific requirements like a portfolio or interview. Degree programs commonly ask for an overall IELTS score of 6.0 to 6.5 or equivalent, but this varies by university and course. For a student visa you'll also need to meet the Genuine Student (GS) requirement.
New Zealand
Universities generally ask for an overall IELTS score of around 6.0 for undergraduate study and 6.5 for postgraduate study, or an equivalent test. You'll need to have completed secondary school for a bachelor's degree, or a relevant bachelor's degree for a master's.
Requirements change regularly, so your counsellor will check the current entry requirements for every course on your list.