The Department of Mathematics at the VU University Amsterdam has a high quality PhD programme, embedded in WONDER, the Dutch Research School in Mathematics. The programme includes some course work, seminars, colloquia and visits to relevant summer schools, but the focus is on training the student to become an independent researcher. Part of the job as a PhD student is to assist with the teaching of courses (for instance in exercise classes).
In the Netherlands, PhD students are considered as academic researchers rather than as students. You need to have a Master's degree to become a PhD student. PhD students get an appropriate salary for a researcher with a Master's degree. Open positions are advertised on the jobs webpage. Positions may be available at any time, depending on the funding situation.
A list of current PhD students can be found here.