If the Yogurt is just expired and not moldy or bad in any other way then eating expired yogurt is safe as long as it's been refrigerated.
If the expired yogurt has mold growing in it or smells bad then throw it out because it could cause food poisoning or stomach aches.
I've eaten yogurt before when it's a few days past the expiration date and I've been fine so just because the yogurt is expired doesn't mean that it's bad.
Check for mold or any other smells though before eating it or if it tastes bad then throw it out.
You can freeze the yogurt and keep it well past the expiration date without any health issues as the frozen yogurt won't allow mold or bacteria to grow on the yogurt.