As we know, the Higgs boson gives mass to other particles. But here is onething which is not clear for me. I mean, I do not understand how the Higgs boson gives mass to other particles? Does anyone could explain me more explicitly how procedure goes that the Higgs boson gives mass to other particles.
The Higgs mechanism gives mass to the spin-1/2 particles in the standard model by forming a condensate which allows particles with different charge to swap helicity. In quantum field theory, a fermionic spin-1/2 particle comes in two helicities, the spin along the direction of motion, and if the helicity doesn't change, that particle is massless. A massive spin-1/2 particle consists of two helicities swapping with each other, and the mass is the rate of helicity swapping. In order to produce a massive spin-1/2 particle, you need two particles of opposite helicity with the same charges, which can flip into each other without violating charge conservation.
This is not the case in the standard model--- the fermions each have different charges, so they can't be massive. But once you have a Higgs condensate, the fermions can flip into each other by absorbing a Higgs condensate particle, thereby changing their charge, and simultaneously flipping the helicity. This process pairs up the quarks and the leptons into pairs which together have a mass. This mass is the helicity flipping rate, and it is determined by the condensate energy density (the Higgs vacuum expectation value) and the degree to which each fermion interacts with the condensate.
For the W and Z gauge bosons, which get mass from the Higgs mechanism a different way, their mass is the Higgs mechanism itself, which is explained on Wikipedia. The Higgs condensate is superconducting for the type of charges which the W and Z are force carriers for, and the relativistically invariant analog of the Meissner effect makes the W and Z bosons short-ranged in the vacuum, just as the ordinary Meissner effect makes the electromagnetic interaction short-ranged in a superconductor.
The Higgs boson is the quantum particle associated with the shaking of the left-over radial component of the condensate field, after the angular parts of the field are absorbed by the gauge bosons. This left-over part still interacts with the fermions proportionally to their mass, so you can tell that the Higgs mechanism is giving mass to the particles just from the predictions this gives for the interaction with the Higgs boson.