Residence Certificate in Bangkok

I want to do the driving license and for that I need a Residence Certificate. I'm here with an Education visa. I tried to get the certificate at my embassy but since I'm still registered in my homecountry they will not issue such a document. They said, I should try to go to the immigration office. Will I get the document there? If yes, what would they want to see? Passport with visa and rental contract? How long would it usually take?

Thanks in advance for your help.