First of all only about 2% of the mass of the matter surrounding us is described by the Higgs mechanism, which should be named Anderson-Higgs-Kibble-Brout-Englert-Hagen-Guralnik mechanism, because all these people proposed it around the same time as a way to provide mass to the fundamental particles (most importantly the gauge bosons of the weak interaction, the W and Z bosons but also the quarks and leptons) without destroying the local gauge symmetry upon which the entire theory is built. Violating this symmetry would make the entire construct useless and contradictory. The other 98% of the mass of the matter surrounding us in everyday life is due to the strong interaction and Quantum Chromodynamics. It is the still not completely understood mechanism of confinement that is creating this mass dynamically. It's, however, known to be the right description from lattice-QCD calculations which leads to a correct prediction of the hadron spectrum within a few percent nowadays, and one can expect this results to become even more accurate with further developments in both hardware and software.
In the Standard Model the mass of the elementary constituents due to the Higgs mechanism is explained as the interaction of the particles with the Higgs field, which has a non-zero vacuum expectation value. By construction this vacuum expectation value is constant in space and time since the vacuum state by assumption is homogeneous and isotropic.
As with any field in a quantum field theory its excitations above the vacuum state should manifest itself as particles, and this was predicted by Higgs, Brout, and Englert and lead to the Nobel prize for Higgs and Englert after the discovery of this Higgs boson. In the meantime more data have confirmed that this Higgs boson has all the properties predicted by the Standard Model. So, indeed, the field can be "manipulated" by smashing protons at the very high energies available at the LHC, and this "manipulation" manifests itself as the creation of the very short-lived Higgs bosons, which can be observed by measuring accurately the energy and momenta of its decay products. The big challenge of the experimentalists is to filter out these decay products from all the other sources, where these particles might come from, and at these energies this "background" is tremendous.