First you must purchase a karoke machine, second get your sim to sing solo after they have picked up the mic. then activate the moveobjects on cheat, third go into buy mode and move the karake machine away from the sim. Fourth unpause the game and then u will see your sim singing with a microphone. But if your doing a movie, u should be aware that sims sometimes jump on the karake machine. P.s. in modthesims.com u can find a custom microphone and use that instead, to do this u must activate the moveobjects on cheat then go to buy mode
after that go into buy mode and delete the microphone.Then activate the boolProp SnapObjectsToGrid false cheat and get the new microphone and place it in the sim's hand!

Hope this was good help!! :D