How is Reynolds Number derived and used?
You can derive the Reynolds number by non-dimensionalization of the Navier-Stokes momentum equation: Wiki link

The choice of reference length and velocity is somewhat arbitrary: usually they are chosen so that they represent "fundamental" dimensions of the study case, e.g.:


For a cylinder in a flow: freestream velocity and cylinder diameter
For a pipe: mean velocity and inner diameter
For a flat plate: freestream velocity and distance from leading edge


In the end of the day, it is a matter of conventions, but what you choose must be physically relevant (e.g. you cannot choose the plate thickness) in a way that, increasing either of them, you go from laminar to turbulent flow. Once the choice of the above pair (length, velocity) is standardized, you can define a critical Reynolds number, which marks the boundary from laminar to turbulent flow (actually, a range of it because of the complex behaviour of fluids during laminar-turbulent transition).