I will send you to a more general physics blog, where a contributor Stephen Wolfram on Higgs, particle physics discusses how the masses enter within the standard model.
Here’s how it basically works. Every type of particle in the Standard Model is associated with waves propagating in a field—just as photons are associated with waves propagating in the electromagnetic field. But for almost all types of particles, the average amplitude value of the underlying field is zero. But for the Higgs field, one imagines something different. One imagines instead that there’s a nonlinear instability that’s built into the mathematical equations that govern it, that leads to a nonzero average value for the field throughout the universe.
And it’s then assumed that all types of particles continually interact with this background field—in such a way as to act so that they have a mass. But what mass? Well, that’s determined by how strongly a particle interacts with the background field. And that in turn is determined by a parameter that one inserts into the model. So to get the observed masses of the particles, one’s just inserting one parameter for each particle, and then arranging it to give the mass of the particle.
That might seem contrived. But at some level it’s OK. It would have been nice if the theory had predicted the masses of the particles. But given that it does not, inserting their values as interaction strengths seems as reasonable as anything.
The standard model does not predict the masses of the particles composing it, so there is nothing to apply. It is put in by hand, and then maybe higher order corrections etc in the case of quarks can play a role in modifying the input values.