It certainly is a departure for many of us raised in a modern urban setting. But mastering this skill has left me feeling empowered, and all the more grateful for all the meat I find on my plate, whether I've processed it myself or not. I appreciate the fact that an animal's life ended to nourish me, and appreciate all the people involved in raising, processing, and preparing it for me.
I think it helps to work alongside someone with more experience at the beginning, either helping them process their birds or having them come help you with yours. There even may be some BYCers in your area with whom you could work.
I think it also helps to look at your meat birds like produce growing in your garden. You tend to its needs with tender care, especially at the start when it's so small and vulnerable. You provide the optimal conditions for good healthy growth, and take pride in its increase. You admire it's natural beauty, and can fill many a pleasurable moment just leaning on the gate and looking at it. You take joy as you see it becoming ready for harvest, and anticipate the satisfaction of nourishing yourself and your family with it.
The essential difference, of course, is the more dramatic ending-of-life when you harvest your chickens rather than picking produce. But when you think of the alternative -- letting the birds continue to live, to have to shelter, feed, & clean up after them until they grow so old they die anyway -- it's as wasteful as if you refused to pick the tomatoes off your bush because you couldn't bear to eat them after watching them grow from seeds. They'd only wither and die anyway, or get eaten by some other animal.
Once you've mastered the method you prefer for dispatching your birds, it's not as awful as you imagine. I make it the final act of kindness I can give my birds, to send them Across The Road in the most efficient manner possible. With gentle handling, hearing soothing words, and being dispatched quickly, effectively, and therefore, most humanely. No predator, not even a disease, would treat them as nicely. They are out in their yard, a familiar setting, being handled by people they know. They have a brief moment of unfamiliar experience, being placed upside-down in a cone, but they don't panic or fuss, just stick their heads out and stare, then -- it's over and they've Crossed The Road.
