The mind/body debate in philosophy got started well before evolutionary theory came on the scene (Descartes evidently thought animals were automata). Debates about the nature of consciousess of course center on the human sort, since that is the one we’re directly acquainted with. But, given we now better understand our close relationship with our non-verbal animal cousins, I am persuaded that animals have first-person experiences. In particular, feelings and emotions appear to be markers of old evolutionary imperatives (fight, flee, eat, etc.), which are likely shared widely in the animal kingdom.
If so, then the “hard problem” of consciousness faces a challenge of accounting for first-person experience in natural systems more broadly than just the human case; the issue can be seen as distinct from others relating to specifically human intelligence and language.
We know about other human minds by analogy with our own. To inform us about animal minds, we would proceed by looking at the neuro-biological correlates of human consciousness, and seeing which have close analogues in the neural structures of animals and which don't. This, of course, can be supplemented by behavioral and other evidence.
The journal Consciousess and Cognition has a new special issue on the Neurobiology of Animal Consciousness. Just what the doctor ordered! Here's the abstract of the introductory article by Bernard Baars:
In humans, conscious perception and cognition depends upon the thalamocortical (T-C) complex, which supports perception, explicit cognition, memory, language, planning, and strategic control. When parts of the T-C system are damaged or stimulated, corresponding effects are found on conscious contents and state, as assessed by reliable reports. In contrast, large regions like cerebellum and basal ganglia can be damaged without affecting conscious cognition directly. Functional brain recordings also show robust activity differences in cortex between experimentally matched conscious and unconscious events. This basic anatomy and physiology is highly conserved in mammals and perhaps ancestral reptiles. While language is absent in other species, homologies in perception, memory, and motor cortex suggest that consciousness of one kind or another may be biologically fundamental and phylogenetically ancient. In humans we infer subjective experiences from behavioral and brain evidence. This evidence is quite similar in other mammals and perhaps some non-mammalian species. On the weight of the biological evidence, therefore, subjectivity may be conserved in species with human-like brains and behavior.
The evidence for human-like subjective experience seems compelling for mammals; less so for non-mammals, but less of the relevant research has been done on those.