So let's first assume you have 24 hours notice.
If your chickens are cooped with traditional poll or plank type roosts, that's the easiest. You just go pluck them off the roost at night. With totes or cages, you should be able to gather them all up in a few minutes if someone is helping you. If they get too woke up they'll get hard to catch and you might have to let them calm down for 30 minutes at a time for every few you catch.
Now let's make them tree-roosting as many of mine do. You can get them one at a time with a long wooden poll. You push the poll up under them and they step onto it. You lower them down slowly then grab them quickly by the legs. If you touch them slowly they often freak out and fly off. Some people put a "T" attachment at the end of the poll. The whole setup needs to be wood though. I've tried it with PVC and they don't like the texture or feel of it and usually won't step on it. It also usually isn't rigid enough for the diameter you'd want to use. I don't find this an efficient way to get a whole flock. But you can definitely get individuals like particular mature hens or a mature rooster you may want to make sure you get.
Now change the scenario to having to catch them during the day.
Again, if they're in a coop, it's easy. Run them down with sturdy nets like the kind you'd catch minnows or butterflies with. With practice, you can catch them up fast this way. They will freak out on sight of the net and you'll have panicked chickens all over. But that is what it is.
A variant of this is to catch them by hand. This takes practice but it doesn't upset them as bad as the net. This is how I usually catch them these days unless it's a mature rooster with long spurs. You can learn to creep up on them without making direct eye contact and slowly moving your hands behind them, then sweeping onto them in a quick movement.
Now if you have free rangers, you can make the scenario a coop situation by training them to feed in a coop. You would daily through them some food in the coop at a set time of day and also use a unique call, word, or sound when you do it. That will condition them to come running when they hear the call and gather up in the coop. Just shut the coop and proceed with a net or by hand.
Or on free range, you can learn to catch them by hand. Habitualize them to be feed as you would in the preceding paragraph to a spot of your choosing in the farm yard. When they're feeding, wade among them. They'll get used to you doing that. Then at the time you want to catch them, call them up, feed them, and wade out into them. Come up behind your chosen chicken while it's distracted picking up feed and preferably while its head is covered by other chickens as they all frantically compete to pick up what you've thrown out. Bring your hands behind them and quickly catch them by the body with your hands covering their wings so they can't flap. You can usually repeat this for several chickens, although the others will see what you're doing and catch on after the first few or several you catch. Regardless, I could catch an entire flock to transport this way in a few minutes, and I often do when trading chickens.
Catching them quickly by hand takes practice. I prefer catching them by the body over their wings so they can't flap. Alternatively I can catch them by the legs, but care must be taken not to only hold one leg. You need to have both legs secure or else the chicken can thrash and twist itself. Maybe even break its leg. I don't like catching by the tail, but some of my Crackers are so wild that's the only way I can get a hand on them. If they twist you need to twist with them so they don't twist their tail bone. You'll mangle their feathers this way so if you like taking pretty pictures like I do, this can ruin a photogenic chicken until the next molt.
Beware a rooster's spurs. I let my mature roosters have spurs as long as they can grow them. I won't tolerate a human-aggressive rooster, but the potential for an accidental serious stabbing is there if a panicked rooster goes to flailing. I usually only catch mature roosters with a net for this reason. Sometimes I can pin one down quickly and push its body to the ground so it can neither run or fly. Then grab it by the legs carefully so I can control where the spurs are and their ability to kick.
Some of my oriental-infused birds are large bodied and can drum me like a turkey. I've had slightly bloody lips before by being struck by the wingbones of big orientals.
