Anyone who hears the Kaddish must answer. In fact, as great as it is to say the Kaddish, answering Amen is even greater. The exception is someone who is in the middle of a prayer that he's not allowed to interrupt. (We'll have to get to those details somewhere else.)
When it comes to Amen, y'hay shmay rabba…, our sages taught us to answer in a loud voice and with all our attention. That doesn't mean to scream—just that we should put ourselves into what we are doing. "Even if a heavenly decree has been signed and sealed for seventy years," the Talmud tells us, "if a person answers 'Amen, y'hay shmay rabba…' with all his power and attention, it will be rescinded on his behalf."
There is also a teaching, attributed to Elijah the prophet, to tack the first word of the next line onto the response, like this:
Amen, y'hay shmay rabba m'vorach l'olam ulalmay almaya…yisboraych