Laying then on their back is the safest- having them sleep on their tummies is not recommended and had been shown to increase the risk of SIDS. Swaddling is great for the first 6-8 weeks as it makes them feel more secure like they are back in the womb. I've done both Co sleeping and had the baby sleep in their crib or bassinet. I think it's whatever works for you and baby.
My daughter sleeps with me too ;-)
You swaddle (you will be shown by the nurses how to do this properly) and just lay baby down. They will stay however you lay them as they don't have the muscle tone to move too much where they will turn on their own. Baby will turn its head towards the way it feels most comfortable.
I did co sleep to an extent with both my first two. I propped myself up slightly with a pillow behind my back, placed a pillow on either side of me and laid them on my chest in a way which their heads were higher than their bodies. Or I laid on my side with them up near my face with a pillow behind them, laying swaddled on their back. I will do the same when my newest addition is born. PLEASE PLEASE PLEASE make sure you are NOT under the influence of any drugs or alcohol and that you are not so tired that you are unaware of your baby! Also, if you KNOW you're a deep sleeper or a heavy mover in your sleep do NOT even try co sleeping.