How do you bring Sims back to life in The Sims 3?

You can't- unless you don't save the game when they die.

You actually can, but it requires an opportunity. If you get a call from the science lab soon after a loved one dies, it gives you the option to bring them back to life. The only thing is, they'll just be a ghost. You'll still be able to control them, though, and make ghost babies.You can also explore the catacombs after dark and use divine interventune to bring them back to life.