To make your tama use the toilet, you'll have to keep an eye on it until it stands in the middle of the screen and has wriggly lines on each side of it. This is the sign that it's about to go to the toilet, so quickly select the icon you usually use to flush. It'll sit on a little duck if it's young, and once it's an adult it'll use a toilet.
But this doesn't mean that your tama will use the toilet all the time once you've done this. You'll still have to clean up after it, unless you're extra good at catching it before it goes.