What's the best way of stopping my Beagle from eating its own poop?

I have a new dog (one year old, one previous owner). She’s arrived with the unpleasant habit of eating her own poop if I don’t immediately clear it up. I can’t always spot it instantly – so, has anyone else had this dog problem? If so, how did you solve it?

For the first time last night she was sick and it was horrifically smelly! I hope she’s learned a lesson from this episode but I doubt it!