In the event of a lesser species rising up to overthrow us, the first thing to do is stay calm. Most other species can sense fear.
Detecting the threat:
This one should be pretty easy. Become concerned if you see any of the following:
Animals exhibiting the ability to use technology (driving cars, using guns, etc).
Animals exhibiting military tactics.
Animals suddenly gaining the ability to speak.
Analyze the threat:
How terrifying is the animal that seems to be evolving?
Worms and insects, while not immediately threatening, could likely bond together to form larger, super-organisms. Ants are the most likely culprit for this.
Whales and fish, while stuck quite large and terrifying, are trapped underwater. This boundary line prevents direct conflict, and may even lead to profitable trade in the future.
Octopus should be carefully watched in this scenario. They’re already basically sentient, and could likely come up with some way to engineer above-water suits to help conquer us.
Dogs (and canines in general) are a major threat. With their prevalence in human society, they’ll have us playing fetch for them in no time.
Cats… Cats are probably already at this stage anyway, but are simply too lazy to do anything about it. Disregard threat if cats are the affected creatures.
Apes, while the closest in appearance to humans, are likely not much of a threat. Their fingers are too large to fit through most trigger guards, and can you imagine a gorilla trying to fit into a sports car?
Determine the cause of the intelligence.
Is it alien meddling?
Was it an artificially induced factor (scientists seem to have this unusual compulsion to make animals as intelligent as humans. This seems quite stupid, but it’s a reality).
Are the creatures simply evolving more rapidly than we expected?
If it seems to be an artificially induced factor, determine what that factor is and come up with a counter in order to return the animals back to their original state.
If it seems to be a naturally accelerated evolution, determine what caused this evolution. Attempt to discern if this same evolution could be applied to humans, keeping us one step ahead of the animals.
If all else fails, contact Washington and instigate a war against all animals.
Alternatively, simply begin polluting the planet. Animals have far less tolerance for pollution than we do, and though this may cause a few civilian casualties, it will ultimately keep our species alive.