Kangaroo care is another term for skin-to-skin holding, and it is wonderful. It's something you should be asking your NICU team about right away, if you haven't started already. Skin-to-skin holding has certainly been around throughout history, but its use for medically fragile infants came about in the 70's in Columbia when equipment shortages forced new ways of trying to help infants survive. Full-time holding and exclusive breastfeeding worked well for many of those infants, and since then the practice has been studied extensively. What the research shows is that it has measurable benefits for babies: it helps babies gain weight, reduces hospital-acquired infections, reduces pain, enhances mother-baby bonding, and can lead to earlier discharge to home. And all you have to do is get your baby skin-to-skin with you, when your baby is stable enough to tolerate it. It's free, it feels wonderful, it is good for baby, it is good for you.... so get started!
Each facility will have their own approach to kangaroo care, but do keep this in mind - some facilities may not yet be up to speed on including kangaroo care. Understand that in some NICUs you will meet resistance.
Nursing staff may still believe it makes the baby too stressed, or it will make their work more difficult. Personally, I am a huge supporter of kangaroo care, and love to encourage parents to plan for it regularly.
If your hospital is reluctant to allow kangaroo care, this is your opportunity to really be an advocate for your baby - print this article, or this one, and share it with your NICU team. Please advocate for what you want and respectfully educate, so that families who come after you will get the best care for their babies too. If it's what you want, stand up for it.
But please also respect that your NICU team has your baby's best interest in mind and will allow it when the time is right. Also, as I have stated before, some NICU parenting jobs may seem scary, and this may be one of those times.
You may feel afraid to hold your baby because she is extremely small, or because she seems unstable. But if the staff tell you that your baby is ready for it, please be brave and go for it - it is worth it! Don't just take my word for it, listen to what this mother had to say in The Preemie Parents' Companion:
"Ben's nurse asked us if we wanted to hold him. He seemed so frail, I didn't think that disturbing him seemed like a very good idea. But the nurse insisted.....I don't really know how toexplain the effect that holding Ben that first time had on me. Maybe it was the first time he seemed real to me, as if he were something more than just a bad dream. I couldn't hold him for long... but that short time proved to be a turning point. My numbness began to fade a bit, and even though I was still worried about what might happen, Ben became mine in a way he hadn't been before. I was, and still am, very surprised at the impact those few minutes had on my feelings. I will always be grateful to that nurse for forcing me to hold my son." 
When you do kangaroo care, plan to hold for at least an hour (which allows for at least one full sleep cycle), and longer is better. Make sure you are well fed, well hydrated, and go to the bathroom before it's time to hold. I would suggest that you do not plan on having visitors during this time - it is for bonding, connection. Turn off your phone. Find out if your hospital will allow you to use a specialty shirt like the NuRoo skin-to-skin shirt so that you can safely sleep with your baby (baby is on monitors) and you can both get much needed rest together. If you find it difficult to sit still for so long, remember to try some mindfulness practices during this long stretch of quiet time. Mostly, just enjoy this beautiful time together.
Please share your kangaroo care stories - was your NICU open to kangaroo care? What was it like the first time you held your baby skin-to-skin?
 The Preemie Parents' Companion, Susan L. Madden, MS, Harvard Common Press, pg 18