Exactly what procedures are followed to increase the luminosity of a particle collider? Say when LHC increases its luminosity, does it increase the number of protons per bunch? If yes, then how?
Luminosity is literally the number of particles, so yes, putting in more of them increases the luminosity.
I think you are perhaps confusing the luminosity of a particular experiment with the maximum luminosity the accelerator can handle. The former is just how much stuff they put in, the later is a function of the design itself.