Once you earn over a certain amount a year (the 'repayment threshold' currently set at $17,160 before tax), you must start making repayments, even if you're still studying.
If you live in New Zealand, student loans are interest free from 1 April 2006. Interest charges will still appear on your statement, but will be written off at the end of each year.
StudyLink is a service of the Ministry of Social Development responsible for Student allowances, Student loans and Unemployment Benefit Student Hardship. They were previously known as Student Services, Work and Income.