How does Higgs Boson get the rest mass?

Higgs Boson detected at LHC is massive. It has high relativistic mass means it has non-zero rest mass.

Higgs Boson gives other things rest mass. But, how does it get rest mass by itself?

Answer

Forget about relativistic mass; it's an outdated and, in this case, irrelevant concept. The Higgs boson has a rest mass of about $125\ \mathrm{GeV}/c^2$ assuming it is in fact what the LHC has found.

Anyway, I would say that the Higgs boson does not actually give other particles mass directly; instead, it's a side effect of the mechanism by which those other particles become massive. It just naturally turns out that the particle produced by this mechanism has to be a massive particle itself.

Or to put it another way, the Higgs field would not be able to give other particles mass if it were not itself massive. Take a look at the "Mexican hat" potential shown in this site's logo. The bump in the middle arises because the Higgs field has an associated mass, the mass of the Higgs boson. That bump pushes the "natural" state of the Higgs field off center, which means the field has a nonzero "default" value, called the vacuum expectation value. It's that vacuum expectation value that gives other particles mass. Without the bump, the minimum of the potential would be in the center, which means the vacuum expectation value of the Higgs field would be zero, which in turn would render it incapable of giving other particles mass.

I'll refer you to another answer of mine for some of the mathematical detail.