What to do with a child that throws fits at everything?

Okay, my granddaughter is only 17 months old. She has spent most of her life with her cousin (in laws) who gets what ever she wants because she throws fits and grandfather doesn't want to listen to her scream. Now my granddaughter who is now living with me does the same thing. I have raised two children and never had this kind of problem before. I have tried everything I know to fix this problem, but am losing my wits about it. When she goes to bed, she throws fits, and I know there is nothing wrong with her. If I stay in the room with her she is finally fall asleep. When she doesn't get what she wants she throws fits, when someone picks up her toys she throws fits. Please someone help me and tell me what I can do about this problem.