Why don't we normally see the Higgs boson? I am a physics student and my dad just asked me about the Higgs Boson. I've told him the little I know, that the Higgs field is a field that is supposed to give mass to elementary particles, and that finding the boson was crucial to see if this mechanism actually did exist. 
After telling that, a question has come into my mind. I have heard that it is very difficult to create the circumstances where we would have Higgs Bosons. I have been told also that this boson is the carrier of the field responsible of giving mass to other particles. So the question is quite natural to me, how come something which "is not there" in "normal" conditions happens to do its work? 
I mean, the carrier of the electromagnetic force are the photons and we have photons in "normal conditions"(by this I have meant not the conditions we have inside the LCH, for example) so it is natural to see their effects, but how is this possible with the Higgs?
 A: The difficulty with Higgs boson is it's high mass, so in order to create it, you need lots of energy (125GeV,   using $E=mc^2$).
What is important to give particles mass is s the Higgs field, not the Higgs boson (which is an excitation of the field). 
The problem is that you have mixed the concept of real particles and "virtual" or "force carrier" particles. The latter can't be observed and can be created spontaneosly, because the energy requiered is "borrowed" via Heisenberg's Principle ($\Delta E\Delta t \geq \frac{\hbar}{2}$). 
Comparing to the analogy you made: two charges will attract/repell, via EM interaction without photons being present. The EM is mediated by virtual photons, but these are not physically observable, unlike "light" photons.
A: It is important to distinguish between the Higgs boson and the Higgs field. The Higgs field is present in all of space and it has a nonzero value everywhere, because that's the lowest-energy configuration, whereas the Higgs boson is an excitation of this field which takes quite a bit of energy to get going.
I'm definitely no expert, but here goes a very simplified picture of what goes on. The Higgs field is (essentially) a complex-valued function of position, $\phi(\mathbf{x})$, which responds to a "mexican hat" potential much like this site's logo.

Image source.
What this means is that the ground state of the field, which has the least energy, has a nonzero value of the field throughout space. This nonzero field interacts with other particles and gives them mass. However, in particle terms this ground state is the vacuum and there's no Higgs boson present.
The Higgs boson itself is an excitation of the field, much like the first excited state of the harmonic oscillator. In it the distribution of possible field values is different, and the energy is higher. This is also the case with, say, photons, with the exception that for all other fields the ground state has zero expected field.
