The answer to the question is: much smarter than people think.
I've blogged about Chaser before. She is a Border Collie who entered the record books when she proved understanding of more than 1,000 English words.
According to the Huffington Post, she has now shown that she understands sentences and grammar. She has been tested with both familiar objects and with new things, and to make completely sure it's language she reacts to, they've also tested her in situations where she couldn't see the objects when she received the command.
Border Collies are considered exceptionally smart, but even the average pooch is thought to have mental abilities comparable to a human two-year-old.
~ Maria Sadowski