Observing animals' behavior (in the wild and through experiments like the one here) and studying how their brains work to see that they often have the same kind of mental features as us (including whichever you'd classify as consciousness) - just at varying degrees of sophistication.

Some would argue that "consciousness" is something non-physical that has no impact on the physical world, and so is not physically detectable or responsible for any behavior, but I feel then it inherently cannot be whatever we mean by "consciousness" that we're directly aware of and talking about in the physical world (because that itself is a physical impact).