I've talked to some current NPSIA students about the co-op/internship process. There is an unpaid internship program run by NPSIA and a co-op program (paid) run by the Graduate office. The internship program happens in December/January with dozens of places accepting applications (DFATD, NGOs, lobby groups, think-tanks). Students pick their top 5 choices and more or less everyone who applies gets a position.
The co-op program happens the summer after first year and you have the option to extend it into your second year. These jobs are usually policy jobs for the federal government. This process is a lot more competitive and you need to pay some money for the application, something like $400, which will give you access to a bunch of counselling services. I've been told that the rate of pay for Master's students is around $18-22/h but I don't if this is still the case.