A few things first...
Some people will tell you to wear newborns with their legs in the carrier, but this puts unhealthy pressure on their ankles and feet so I do not recommend it. In the video you'll see it is completely possible to safely wear even the newest of newborns with their feet out.
You'll notice in the video before I pull the bottom rail up between the baby and I to create a good "seat" I actually pull most of the fabric up along his back. You do not want a lot of fabric bunched up in your baby's knees especially with a newborn because it can inhibit circulation.
Newborn-wearing isn't easy. Their legs are tiny and they're floppy and have no head control. But if you have a baby who insists on being held 24/7 it can save a new parent's sanity. Just keep practicing and it will get easier. Remember to always practice with a happy baby! The best time to start trying a new carrier with any age baby is when they have a fresh diaper and are freshly fed. The happier they are the easier it will be.
Newborns don't have any neck control and the muscles in their throat are still barely developed. You have to make sure they don't go chin to chest to prevent suffocation. This is true for any scenario (in a swing, car seat, anywhere) not just a baby carrier.
You'll notice I'm using the ring sling that I dyed and sewed for my friend in the video :-)
The following screen shot is just so you can "pin" directly to this page...