Work while you study
It's not mandatory to learn Dutch, but it will greatly improve your chances of finding a job. Many employers won't hire you if you're unable to understand and/or speak the Dutch language at a fair level. Jobs where English is the main working language are in the minority.
Even though the English language is widely used in the Netherlands, it does not have an official status. This is why at most companies, even those operating internationally, Dutch is the main working language.
Working as a non-EU/EEA student
Only your employer can apply for the work permit before hiring you. The work permit must be applied for at the UWV Werkbedrijf, and the procedure will take approximately 5 weeks. There are some documents that need to be included with the application for a work permit. These can be checked on the UWV website, under ‘werkstudent’.
All in all the procedure is fairly uncomplicated, since it is not necessary to demonstrate that the job position cannot be filled by a Dutch or EU/EEA citizen. Please note that you cannot start working before the work permit has been issued. Starting earlier will result in your employer being fined by the government, and you losing your residence permit!
Yes, you can do an internship, as long as it is relevant for your studies. Please also check with your programme for all the options. It’s important to conclude an internship agreement before you start your internship.
How to find a side job
Depending on your income you might be eligible for a compensation to help you cover the costs of your Dutch public health insurance. This compensation is called ‘Zorgtoeslag’ in Dutch (healthcare allowance or benefit), and you can read more about it on the website of the Dutch tax authority.
Your employer will withhold taxes and social insurance (look under 'Things to arrange after you started your job - Income and taxes') contributions from your gross wage. The net amount you receive will depend on how much is withheld.