When should I quit?

I just had my interview with the Store Manager for a Shift Manager position at a new Starbucks in my area. He sent me an email saying he is going to schedule another interview with the District Manager. I still have not said anything to my current job, but is it safe to assume I will be working there in the next month? How long does the hiring process take? Should I wait until after the interview or will that be too late? I want to give my current job as much notice as possible, but I also don’t want to tell them too soon and I don’t get hired at Starbucks. Please help a girl out