I LOVE ring slings, I haven't even tried other carriers. I am on baby number two with them.
And I think learning to carry the newborn with them can be tough sometimes. I agree with the others that tightening is the key with the itty bitties. I prefer a tummy to tummy and have always had a hard time with a cradle hold. Though, occasionaly, I have had a tummy to tummy morph to a cradle, as she would slide sideways and I would tighten and adjust and before I knew it, cradle hold lol
This is almost exactly how I get little ones settled into the sling:
Put the sling on with the rings in the hollow of your right shoulder, where you would place a corsage. Spread the fabric out over your shoulder, make a nice deep pocket etc. Basically get it all ready before you pick up the babe.
Put the baby in and make sure she has a nice deep seat ie there is plenty of fabric between you and her. Then use your left forearm to hold her in place while you use your right hand to pull the top rail up to her shoulders. She will be kind of sitting on your forearm. With her still sitting there, use your right hand to pull the fabric tightly towards your right side. Hold it there with your left hand (forearm still holding babe). Then use your right hand to pull the tail of the sling to take up the slack you're holding in your left hand. Do the top and bottom rails separately though, don't just pull the whole tail. Keep adjusting like this until everything is nice and tight. Carefully take your forearm away and let the sling take her weight. If it still feels a bit insecure keep adjusting the top and bottom rails until it's tight enough.
The only thing I do different is that if it's a sling that isn't already prethreaded for me, I pull the whole tail first to get that genearal adjustment, then I adjust the top and bottom rails (and the middle sometimes, I don't like a pocket that is too deep compared to the rails) seperately as needed.
One other tip, I try to keep the top rail sitting along the little one's head along the ear, with her face turned sideways, so that her head is supported well and her nose isn't smooshed into my chest. It's tough though because they are so tiny and it's so easy for that rail to slip down.
Basically, I find newborn wearing does require regular adjustments, and they slip, slide, wiggle and flop around some.