Actually, it is a good question. Properly counting the age can be important: some states specify the age a pup can be before it can leave its mother, airlines have a minimum age for shipping, etc.
I have always counted week-to-week. If the pup was born on a Saturday, I look on the calendar and count Saturdays since it was born, starting with the Saturday 7 days after the pup was born.
Here in South Africa we have no age limit for separating a pup from its mother
but the airlines won't ship a pup under 8 weeks, so proper counting of the age matters!