At least 7 days of active pills. Depending on the brand, when you start your packet you normally start on the sugar pills (normal oral combined pill, mini pill (progesterone only) is different). So make sure that you don't start counting the days till you have started on the active pills.
Just as a side note, the worst ones to miss are either at the end of the packet or the beginning of the active pills.
The product information sheet will have all this info. You should find it in your packet of pills. If not ask the pharmacist or google the product info.
I cant believe your doctor didn't talk to you about that.....
Usually you have to use an alternate form of birth control (condoms) for a week, then you should be fine. The pamphlet that came with it should have more detailed info.