I raised my first batch of Freedom Rangers for meat this summer and have butchered all but 8 of them now in three "batches". Like you, I was completely new to the idea of butchering, not having done the deed with game or even fish before.
My advice is to educate yourself as well as possible by googling articles on "how to butcher a chicken" watch some youtube videos of the actual killing as well as the butchering and decide what method you want to use. Then get all of your equipment set up, water on early to get it up to the proper scalding temperature. Make sure you have at least one very sharp knife, and I mean very sharp. I ended up purchasing a new one after my first attempt. Review the articles or videos again and make sure you have all the equipment you need.
On actual butchering day you have to have resolve. One thing I learned...sort of the hard way, is that there is no gentle way to kill a chicken that you intend to eat. You can be gentle in the way you catch the chicken, you can be gentle in the way you handle, carry and talk to the chicken as you bring it to whatever apparatus you've set up for the kill, but when it comes time to kill it, you need to be decisive and quick and through. If you try to be gentle, you'll probably prolong the process, making it harder on the chicken and harder on yourself.
Be prepared to feel bad about it. Even if your logical brain knows you are doing a good thing, and that your chicken is meeting a much better end after a much better life than it would have had in a commercial farm, your emotional side may not listen to any of your logic, but you'll have a very supportive group here on this forum who will provide their wisdom and empathy and help you learn by the experience.
While I can't say I'll ever be casual about the killing part (and I really don't think I ever WANT to be casual about it) there is something deeply satisfying about the end of the day, when I have a huge pot of stock on the stove, 6 - 8 chickens waiting to go into the freezer, a lovely batch of chicken-liver pate to spread on some nice French bread and a bunch of tasty giblets put aside for dog-training treats. That and the knowledge that even a city-bred girl can be tough and resoursefull and do what needs to be done.