If you're a non-EU international bachelor or masters student at the VU, it is possible to bring your partner and/or child(ren) to the Netherlands. However, you will have to apply for their visa and/or residence permit yourself as you will be their sponsor. VU Amsterdam can't process this type of application for you.
You can find more information about the process, required documents and cost of the application on the website of the IND. You can find more information about applying for a partner here, and more information about applying for children under 18 here. The IND takes up to 3 months to make a decision on your application(s) and this process cannot be expedited.
If your family-members or partner come to the Netherlands too, you function as their legal and financial sponsor. In this regard, you also have an information, administration and retention obligation. See the IND publication called "Enabling a family-member or relative to come to the Netherlands" here. It is also important to note that your family member or partner is not allowed to work at all with the residence permit they will receive.