We skinned the first couple chickens we raised, that was few years ago. I have to say that a chicken without the skin is not worth it in my opinion. The skin is one of the most flavorful parts - not to mention that you loose some good wing bones (aka stock/broth making material) in the process. We have a plucker now because we raise 250+ birds a year these days, but before we got the plucker, we decided early on that plucking them by hand was worth it - albeit time consuming. Like the other replies have mentioned- scald the bird in hot water between 145-153F (this specific range of temperatures is important). Move it around while its in the scald water to get the water to penetrate the feathers (remember feathers are designed to repel water so you must agitate the water/bird to get a proper scald). Test a single, thick tail feather to make sure the feathers pop out easily. It might take a couple birds to figure out the perfect scald process. Then hang the bird by its feet and pull the feathers out in a downward motion (against the "grain", if you will). Once you get most of them off, pinch the remaining downy feathers off - all the feathers should come off easily. Keep a hose with spray nozzle handy to spray the bird occasionally while plucking - it helps keep the loose feathers from sticking to the bird and making it hard to see which ones still need to come out.
Cheers to your second butchering! After a few seasons, it will become second nature and you'll be able to show others how to do it like a pro. Expect to be butchering all day since it is your first time and you will be hand plucking. Also, two people makes the plucking go twice as fast (obviously), and that can be really helpful in terms of how long the day goes on. Take your time and have fun!
PS: the fastest hand pluckers (there are real competitions) can pluck a chicken in under 3 minutes. When my partner and I were practiced at it, it took the two of us about 5-10 minutes per bird to get it picked clean.