I believe you are talking about pullets. Cockerels are different, the hormones of puberty have a strong effect on the boys. I believe the chart
@Molpet gave is for cockerels but those ages look pretty old for many people used to the chicken from the store? I can't recall ever seeing a chart that focused on pullets only.
How do you plan to cook them? That has a big effect on what age you butcher them. If you use a hot and dry cooking method like frying or grilling they need to be fairly young to be tender. When they get older they need to be cooked with a slower moister method, like baking. Old birds can be used in soups or stews or cooked in pressure cookers. Coq au Vin is a method the French developed to make a gourmet meal out of an old rooster. Chicken and Dumplings made with an old hen is comfort food.
Before you cook any chicken you need to age them to get past rigor mortis. That's where the body goes stiff after death. You want to be able to wiggle a joint without it being at all stiff. How fast they pass rigor mortis depends some on the age of the bird and also the temperature. While they are aging they need to be cool enough that bacteria does not grow. Some people age in the refrigerator, some in an ice chest on ice.
That's because there is no one simple answer, way too many variables for that. I can't give you any simple answers that will cover every chicken in the world and every situation.
I start butchering my cockerels at 16 weeks as I decide which I want to keep. I make my final decision and butcher the last one at 23 weeks. That suits my goals for raising them and the way I cook them. They typically have finished "fast growth" by 23 weeks and have enough meat to make it worthwhile butchering them by 16 weeks.
I butcher my pullets around 8 months. I want to evaluate their laying before I decide which to butcher. I'll also eliminate any that have defects or behaviors I don't want in my flock. By 8 months I have a pretty good idea of which ones will lay a decent amount of eggs of a decent quality and will not disrupt the peace and tranquility of the flock.
I bake my cockerels and pullets. Piece them out and put them in a covered dish with herbs, onion, carrot, garlic, and celery. Cook at 250 degrees for 2-1/2 to 3 hours. Carefully remove with a slotted spoon as the meat can fall off of the bone. Strain the liquid and de-fat it. You should have a half cup to a cup of the best broth you've ever had.
Any way you can. There are a lot of different ways to kill a chicken for butcher. Your method needs to be sure. You don't want to close your eyes or flinch at the wrong time. You may only injure the chicken instead of getting a clean kill or you may injure yourself. Some people can use certain methods better than others. With any method you often have problems the first time you do it but it is usually a very quick learning curve.
The killing cone as described above is very popular on here. You put the bird in with the neck sticking out. Some people cut off the head with pruning shears or loppers. Some use a sharp knife to slit the throat and bleed it to death. You need to learn the details of which shears to use or where to slice the throat. There are always details.
I use the hatchet and stump method. I don't recommend this to most people but I grew up clearing fence rows and turning wood into kindling. Driving nails and fence staples with a hammer. I can hit what I aim at. There are tricks to this also. Ask if you want the details.
The broom method is fairly popular. You put the neck under a broom and hold the broom down with your feet then jerk the bird by its feet.
There are other methods. You need to choose which one you think you can do without flinching or hesitating. Good luck!
