Virtually all of the needed velocity is tangent to the surface, not away from it. So you can accelerate the vehicle along the ground at least part of the way, and only then turn heavenward and burn fuel to get into orbit. With this boost you significantly reduce the amount of fuel needed.
There are many way of doing this. You can have magnetic propulsion (very futuristic and powerful), you can have a simple motor on the vehicle, powered by contact with rails on the ground (but motors have a limit of how fast they can work). You could have fuel "guns" fired into the back of the vehicle as it passes them, which would then capture the container and burn them as a normal rocket would. This has the benefit of not requiring a large rail, just fuel stations that the rocket would pass over.
These are just some basic ideas, there are many more.