Thanks to the heroic efforts of thousands of experimental physicists, engineers and technicians we have learned that the Higgs field is real. Experimental exploration of the Higgs field and its quantum Higgs boson is an ongoing effort. At this point, it seems that the next generation of particle colliders known as Higgs factories will be necessary to learn the details of the Higgs field. Having said that, it is important to point out that physicists have made great progress.
W and Z bosons (force carrying particles of the weak-nuclear-force) acquire mass as a result of spontaneous (local gauge) symmetry breaking involving the Higgs field (Brout–Englert–Higgs mechanism) .
Fermions (excluding neutrinos) acquire mass through their Yukawa couplings to the Higgs field. Neutrinos are fermions too but it is a big question whether they get their tiny masses from the Higgs field.
Photon and gluon are massless particles. They interact with the Higgs field as well but remain massless.
Proton and neutron are not elementary particles, they are composite of quarks and gluons, therefore their masses primarily come from the interaction energy of quarks and gluons.
Yukawa coupling of fermions to the Higgs field is a novel type of coupling that cannot be described as the spontaneous breaking of a gauge symmetry.
“One of the most striking results of the LHC exploration was the discovery of a completely new type of force. Before the discovery of the Higgs boson, we knew of four fundamental forces governing natural phenomena (strong, weak, electromagnetic forces and gravity). All of them were successfully deduced from a single conceptual principle – called ‘gauge symmmetry.’ In the meantime, the LHC has discovered the existence of new forces in nature. These forces control how the Higgs boson interacts with quarks and leptons and, so far, the LHC has identified their effect on top and bottom quarks and on tau leptons (the so-called ‘third generation’). According to the Standard Model, these new forces are as fundamental as those previously known, but of a different nature – not ‘gauge-like.’ While the Standard Model properly describes these forces, it is silent on the origin of the many free parameters associated with them or on any deeper explanation of their complex structure.” – Gian Francesco Giudice 
Higgs coupling strength to fermions is proportional to the mass of the fermion.
Higgs coupling strength to the gauge bosons of the weak-nuclear-force is proportional to the square of the mass of the gauge boson.
Experimental verification summary
The number of “sigmas” measures how unlikely it is to get a certain experimental result as a matter of chance rather than due to a real effect. In particle physics, discovery requires at least 5σ statistical significance. The “5σ” means there is 1 in 3.5 million chance for the result to be a statistical error.
The summary below does not include neutrinos.
Higgs coupling to third generation of fermions
“5σ observations of its coupling to the tau lepton in 2015 and to the top and bottom quarks in 2018, all of which are third-generation fermions.” .
Higgs coupling to second generation of fermions:
Second generation fermions are: muon, c-quark, s-quark (and their anti-particles).
“Couplings to the second generation of fermions are much weaker and neither ATLAS nor CMS have so far observed Higgs transformations into charm quarks, strange quarks or muons. The next run of the LHC (2021 onwards) is expected to provide enough data to begin to shed light on some of these interactions.” 
Actually, there is some progress on the Higgs coupling to muon.
“The first evidence for the coupling of the Higgs boson to a second-generation fermion, the muon, has been reported at the LHC. At the 40th International Conference on High Energy Physics, held from 28 July to 6 August , CMS reported a 3σ excess of H → μμ decay candidates compared to the expected sample under the hypothesis of no coupling between the Higgs boson and the muon. A similar analysis by the ATLAS collaboration yielded a 2σ excess for the coupling.” 
The experimental verification of Higgs coupling to muon is not official yet because statistical significance is not 5σ yet.
Higgs coupling to first generation of fermions:
Experimental verification of Higgs coupling to electron, u-quark and d-quark will be extremely difficult to establish due to overwhelming background noise.
Higgs coupling to W and Z
“Its couplings to W and Z bosons have also been established at 5σ confidence” 
Higgs coupling to gluons
Remember that gluons are massless. This may give you the wrong impression that the Higgs field does not interact with gluons. The opposite is true.
“And, while transformations to gluons are impossible to observe, the scientists could probe this coupling through the Higgs production itself: the most abundant way for a Higgs to be created in proton–proton interactions is for two gluons – one from each proton – to fuse together, accounting for nearly 90% of Higgs bosons produced at the LHC.” 
Higgs coupling to photons
Photons are massless. Again, this may give you the wrong impression that the Higgs field does not interact with photons. On the contrary, Higgs boson was discovered from its decay into two photons.
“Indeed, the Higgs decays to photons very rarely. If the Higgs boson mass is about 125 GeV, and you make 10,000 of them, less than ten will decay to two photons. Most will decay to bottom (beauty), quarks. But these are very hard to distinguish from other collision debris which don’t involve a Higgs.” 
A Higgs boson decays to two photons via a quantum loop. Therefore, it is not a direct decay to photons. Regarding the intermediate quantum loop:
“gluon-fusion production mechanism and the Higgs transformation to photon pairs require the creation and annihilation of virtual top–antitop pairs.” 
 Brout–Englert–Higgs mechanism
 Gian Francesco Giudice, “On Future High-Energy Colliders”,
 Mark Rayner, “Turning the screw on H → μμ”, CERN Courier,
 Achintya Rao, “The Higgs boson: Revealing nature’s secrets”,
 Jon Butterworth, “Higgs boson in massless-particle coupling shock, and other stories”