The natural question, upon the occasion of the birth of the royal baby is: How long until this tiny infant becomes King? And the answer is: November 6, 2060, when he is 47 years old. How do we know this? Because of math and guessing, naturally.
The way the British monarchy works, in rough terms, is that a new monarch is crowned upon the death of the existing one. At birth, there will be three people in between Little Baby Whomever and the throne, all of whom will need to die (or abdicate, which seems unlikely, Belgian example notwithstanding) before Whomever's reign can begin: First, Queen Elizabeth, then Prince Charles (Whomever's grandfather), and then Prince William (Whomever's dad).
So how can know when all of that will happen? The short answer is: we can't. But the long answer is: we can guess by looking at trends.
One trend that isn't helpful is the history of ascension in the English/British monarchy. Looking at every king or queen back to Æthelstan, born in 895, gives us the following picture of the monarchy. Each monarch has a vertical bar. The yellow section is his or her life prior to assuming the throne; the purple, the part after ascension until death. (We've included Elizabeth II at far right, extending the purple to 2013.)