One day in the near future, plans for a dimensional transporter are released for free on the internet, something so easy and so cheap that children can build it.  When you flip the switch, you move over to another Earth, almost exactly the same as ours except people never evolved leaving it in its unadulterated state.  Flip it again and you go to the next one, on and on.  You can go in two directions, sort of like the number line with positive and negative numbers.  This instantly solves most of Earth's resource problems and overcrowding issues.  There are some minor inconveniences: you can't bring iron in metallic form, and you get pretty nauseous for a while after "stepping". But other than that, the worlds are there for the taking.

There is one man who can do this without a device, totally on his own, and he is famous for having stepped farther than anyone else, thousands of Earths away.  When he gets back to the "real" Earth, his is commissioned by a Tibetan mechanic reincarnated into a supercomputer to go on the longest expedition yet.

They find more than they expect.  There are others out there moving towards our Earth, and they are running from something...

The Long Earth has a classic science fiction feel: this is a story of exploration.  There is no action set pieces, no major violent incidents with lasers and giant spaceships.  (There are in fact no spaceships, though there is a resourceful super-robot.)  This is the first part of a two-part story, and it shows.  It feels like the authors are leading up to something that never quite arrives, but a planned follow up should satisfy those points.  As a reader familiar with Terry Pratchett's work, I can tell which bits are his, but this is nothing like his usual work.  I can't speak to Stephen Baxter's contribution, though this may lead me to read some of his stuff.