Ira was 6 days old the first time I wore him, and it worked like a charm. He slept the whole time, and he was nice and warm all zipped into my jacket.
The Moby wrap is basically a really long piece of fabric that gets skinnier toward the ends that you wrap around yourself and then put your baby into. You can carry them like I have Ira in the above photo, you can carry them facing you with legs out (with fabric between you or not), and you can do a hip carry when they're older. Moby actually has really easy instructions here.
The biggest complaint that I have heard from people about the Moby wrap is that they can't figure it out, or that it's hard to use because it's one long piece of fabric. I can totally relate, especially if you're new to baby wearing.
Here's what I recommend: wait until your baby is full and happy, maybe even asleep if he's still teeny tiny and can be moved around without waking up. If your baby starts screaming because he's otherwise mad about something, you're going to curse my name and all things baby wearing.
Start when you're at home, either by yourself, or with just one other person to hold the baby or help you wrap. Don't wait to bust it out in front of the in-laws, your cousins, or all of your friends from work who just came over to hang out. You'll be stressed, you'll try to learn it too fast, and you will (again) curse my name for recommending this blankety-blank wrap.
Also, when you're ready to put the baby in, stand in front of your bed so you won't be stressed about dropping the baby. Of course you aren't going to drop the baby, but it's a lot easier to be relaxed if your baby is over a high bed rather than over an asphalt parking lot, or your kitchen tiles.
If you wrap it and it doesn't feel right to you, take the baby out and try again. As long as your baby will work with you, keep trying it. It might take one or two tries to figure out how you're both comfortable in it.
To wear a newborn in your Moby, you wrap it onto yourself and then put your baby's legs in the "froggy position" (like they want to be anyway) and pull all the fabric around them. If your baby is older, you're basically doing the same thing, except you're letting their legs hang out.
If you have a brand new baby, this carrier is one of my favorites, because it keeps your baby warm no matter how chilly it is outside. Even if the weather is warm, if your baby is anything like mine, he likes to be a little hotbox.
I also like it because it's a one-size carrier - no need to buy a bigger one if dad wants to use it.
It's a very secure carrier, and one of my first choices if I'll be doing chores, cooking, or wearing for a long time. I feel like Ira is really comfy in it, and the fabric is soft and doesn't seem to aggravate his skin, even when I'm wearing for a long time. It's also nice because it's a one-size carrier....I can wear it, PB can wear it, and Mimi can wear it.
The only drawbacks are that the tails are really long, so I don't like to use it if we're out and about too often. Nobody wants their tails dragging in the Walmart parking lot. Barf. Also, now that I have a 15 pound chunky monkey, I have to tie it pretty tight or it feels like he's sliding down in it/stretching it out a lot. Technically you can use it until baby is 35 pounds, but I can't imagine how much he'd stretch it at that point.
The Moby is still one of my favorite newborn options, and one of my favorite cold weather options! Definitely deserves a place in your baby-wearing stash.