Do I charge my first client before or after the design is complete?

This is my first serious client and their first design experience. I am designing a Logo and a business card for them. We haven't discussed price yet and I haven't started on their design either, so i'm wondering when I should charge them? Before I begin or after?

Also, How should I charge them if it's the first design experience for the both of us? More specifically , should I charge them based on the time it takes to design or a flat fee?