Usually by truck for at least part of the journey (airplanes, boats, and trains are also commonly used). They are carried in custom built frames that hold them in the correct orientation. The frame is then surrounded by a sealed box that keeps the satellite clean, and with the appropriate climate controls (temperature, humidity, etc).
Here's a good overview of the process (though in this case it's a satellite that can safely be transported in multiple orientations): https://qz.com/1346279/big-plane/
It just seems to me that it would need to be horizontal, and likely encounter greater stresses during transport than during a tightly controlled horizontal assembly process.
Here's a good overview of the process (though in this case it's a satellite that can safely be transported in multiple orientations): https://qz.com/1346279/big-plane/