If your guitar starts to wobble around, or worse still, does a face plant, then you're probably not holding it right. You should be using your strumming arm to hold it against your body. Some people use their bicep to clamp their guitar towards their body, but I prefer to use my forearm.
Is there a wrong way to hold a guitar?
The index and thumb is the generally accepted way of holding pick, but that doesn't mean it's the only right way. Personally I think the best way of looking as it is that there's no wrong way of holding the pick so long as it doesn't hinder your playing ability to play or cause unnecessary tension / discomfort.
Is there a right way to hold a guitar pick?
Slide your pick between your thumb and the middle of your index finger. Keep a relaxed grip on your pick with the pointed end sticking out away from your hand. Your pick should be held under the center of your thumb. You typically want to leave about a half inch of your pick sticking out from beneath your thumb.