How do migrating birds appear to sense magnetic fields?

Through a light-sensitive protein in the eye. Cryptochrome absorbs blue light, which knocks an electron into a state where the pair's spins are affected by the surrounding magnetic field, which changes the chemistry that follows - so the field alters a visual signal. On that model a bird does not feel the field, it sees it, as a pattern superimposed on its view.

The evidence is indirect and strong. Migratory birds are disoriented by weak radio-frequency fields at exactly the frequencies that would disrupt the quantum spin mechanism, they need light of the right wavelength to orient at all, and the effect depends on the eye rather than the beak - though iron-based receptors in the beak have also been proposed and have had a harder time replicating.

If it holds, it is the clearest case of quantum mechanics being used biologically. Spin coherence is normally destroyed almost instantly at body temperature, and a warm wet cell maintaining it long enough to be useful is exactly what physicists would have said was impossible - which is why quantum biology went from a fringe phrase to a field on the strength of it.