Resident Parking Permit in Budapest for Non-EU student

You need to bring in your car papers and address card into your local city hall and pay a fee for the year.Bring your tax ID card too.
They handle parking stickers which is all electronic these days, no actual sticker needed to place on the windscreen.

Thank you for your reply.
but would my Non-plastic address card work as the immigration office gave me that.

I don't know what exact immigration card they need but if that's all you have then that should be enough.
I forgot to mention your car must be insured , registered and have plates before getting the parking permit.

It's quite streight forwards to do. You need your residence card, address card, passport and all the car documents and you take them to the parking permit office in your area. You fill in a form have your documents checked and pay a yearly fee. The year begins in January so if you do it in November you only have two months for the same price.
Just look up parking permits budapest on the net and it will give you the list of offices. You go to the one in your district. If not there will be a central office.