"Well, there you are, boy. Platform nine -- platform ten. Your platform should be somewhere in the middle, but they don't seem to have built it yet, do they?"
     -- Vernon Dursley

"All you have to do is walk straight at the barrier between platforms nine and ten. Don't stop and don't be scared you'll crash into it, that's very important. Best do it at a bit of a run if you're nervous. Go on, go now..."
     -- Molly Weasley

Atlas of Wizarding Britain: map of Platform 9-3/4

In order to catch the Hogwarts Express train to Hogwarts, students must board at Platform Nine and Three Quarters at Kings Cross Station. This Platform is not visible to Muggles. In fact, you get to it by running toward the solid barrier between Platforms Nine and Ten, full tilt. Instead of hitting the wall, you'll find yourself passing under a wrought iron sign that says "Platform Nine and Three Quarters." A scarlet steam engine waits there, with a string of red passenger carriages behind it, with a sign overhead saying "Hogwarts Express, 11 A.M." A guard sits near the ticket booth, monitoring the comings and goings through the portal, making sure that too many people don't do it at the same time and alarm the Muggles. On days when the train is set to leave for Hogwarts, the Platform is filled with Witches and Wizards saying good bye to their children. Cats and owls are a common sight among the crowd.

JKR admits that she actually made a mistake when she placed Platform 9¾ at King's Cross Station: “I wrote Platform 9¾ when I was living in Manchester, and I was actually thinking of Euston. So anyone who’s been to the real Platforms 9 and 10 at King’s Cross will realise they don’t bear a great resemblance to the platforms nine and ten as described in the book, and that would be because I was thinking of Euston at the time." (HPM)

The platform actually used for filming at King's Cross Station is Platform 4. Hagrid and Harry are also filmed walking over the pedestrian bridge across the tracks.