When should my period start after getting of the pill?

Okay, so I was late in getting my prescription renewed for my birth control and have gone a full month without it. I just got my prescription refilled and my doctor told me to take it it when my period starts which was suppose to be soon. It hasn't started and from my research it might take up to 6 weeks for my period to return after "stopping" birth control (pill). When should I start my new pills? I'm not really sure what to do!!