"Funny way to get to a wizard's school, the train. Magic carpets all got punctures, have they?" 
     -- Vernon Dursley

The Hogwarts Express is a passenger train which makes a run between Kings Cross Station, London, and Hogsmeade Station near Hogwarts. It makes this run at least four times a year, and probably more often than that, as needed. It does leave without fail on September 1 at 11 am from Platform Nine and Three Quarters, Kings Cross, arriving at Hogsmeade in the early evening. Most students take the train back to Kings Cross to go home for the Christmas and Easter holidays. The train also makes the run back again to London at the end of term in June. 

The train is pulled by a scarlet steam locomotive. There is no dining service, but a witch pushes a tea cart through the train midway through the trip, selling various types of candy and iced pumpkin juice. There is a separate car or two at the front of the train for Hogwarts Prefects. There are usually no adults aboard the Hogwarts Express except the witch with the tea cart and the driver.

In the film, the number on the engine is 5972 (SS/f).

How does a scarlet stream train travel the length of Britain without being seen?

The Hogwarts Express is not really a steam train. It does look like one and it acts like one in certain key ways, but it isn't one. It's a magical device. It borrows its form and it's intended function from real steam trains, but not the technology. It's like the Ministry Cars, the Knight Bus, and Wizarding Wireless, which also borrow their form from Muggle technology but which are magical devices. 

Wizard "machines" aren't Muggle machines. They don't work on petrol or coal or electricity, they work by magic. In some cases, such as the Hogwarts Express, they are copied from Muggle machinery (and in this case it's clearly a copy of a Muggle device, since many parts of it would have no function in the Wizard version, but there they are, clearly copied from the Muggle original without an understanding of what those parts were for). The Hogwarts Express, powered by magic, goes where it's supposed to because that's what it's supposed to do. Magic is more than anything else intention made reality. The Hogwarts Express chugs away up north because it is magicked to do so. 

So what about the track? Someone on the HP4GU list some time ago came up with a perfect and wonderful solution: the Hogwarts Express uses existing track for most of the journey, but just squeezes past the other trains on the line or cars at the crossings. It follows the same pattern as the other magical transportation devices we've seen, the Knight Bus and the Ministry Cars, and just somehow manages to jump/squeeze/slip through. It's not heard or seen by Muggles because, as Stan Shunpike points out, "they don't hear nuffink, do they."

The driver and the guard and the witch with the cart are the equivalent of Ernie Prang and Stan Shunpike: trained to operate magical devices using magic without really understanding the technology from which their devices are copied. Ernie shifts the wheel back and forth but doesn't really steer the bus along the road specifically, he's making the magic work. One turn could send them to the left side of the motorway or halfway to Torquay, depending on what he intended it to do. 

The train itself looks like a train from the outside and pretty much looks like a train on the inside, although I think it's likely that it adjusts it's interior dimensions for the task at hand (there is always one more compartment, but never an extra, it seems). Unlike the Knight Bus, which looks fairly similar to a bus on the outside but nothing like a bus on the inside, the Hogwarts Express seems to be to most appearances a real train. But it isn't. It's magic.