In days past, the government used to encourage, and even BEG citizens, all of them, to keep their own backyard flock. During wartimes, a massive campaign was launched by the Department of Agriculture telling people how to raise chickens, grow a garden, and put up their own food. Now, it's much more common to have to fight local government for your rights to do any of those things. All across the nation, there are entire towns and counties that have strict no(or very limited) chicken policies, so it's very important that you check BEFORE you buy those chicks at the local feed store.
What can you do if your area is a fun free zone? Start by figuring out exactly when, why, and by who the law was passed. Inquire with those in charge about what needs to be done in order to change their minds, and get involved. Don't forget to get others involved in the cause as well. It's almost guaranteed that there are others just as perturbed as you are that there is a ban.
Now that we've tackled that beast, lets talk about where to begin with the actual flock. First you'll need a place to put them that is safe, dry, and draft free. Ideally it will be mobile so that the chickens can be moved to different areas to be given access to fresh grass and bugs daily or weekly depending on flock size. If you would rather keep the birds stationary, there is nothing wrong with that, but for the purposes of this post we will assume they will be mobile.
A good mobile coop doesn't need to be incredibly large. The chickens will only be in there at night, and periodically to lay eggs. You'll need roosting bars, a hardware cloth bottom, and two or more nest boxes that can be accessed by humans from the outside. Two large wheels and a solid locking door and roof, and you're set.
Now, unless you have a well fenced yard, you can't just let the chickens out to roam around to their own devices. Doing so is irresponsible both as a chicken keeper and as a neighbor. Even if you have acres and acres of land, "free range chickens" is just code for wildlife buffet. Time and time again I see complaints about raccoons, foxes, coyotes, and bobcats killing chickens. The aforementioned wildlife are then blamed, trapped, shot, or relocated all the while the owner makes no improvements to the safety of their flock. Don't be that person. If something is killing your livestock, it is entirely on you to prevent such things from happening and wildlife isn't to blame. My personal solution to this is electric poultry netting. Its easy to erect and move. Premier One Fencing has an excellent selection of fencing and solar chargers, and I highly recommend them with no affiliation.
Another solution to keeping your flock mobile and protected with no fencing available is to build an enclosed run onto your mobile coop. this can be as simple as an A-Frame with hardware cloth or as complex as an expandable chainlink cage on wheels.
Once you are completely sure you have a secure place for your flock to live, it's time to set up the brooder and purchase chicks (preferably not in the same day.) You'll need walls about 2 feet tall, a breathable top, a heat lamp or the safer option, a brooder plate, bedding, a feeder, and a waterer. For food, you'll need a chick starter. If you're ordering chickens from a hatchery, you'll have the option of getting them vaccinated for coccidiosis. If you choose this, you MUST NOT feed the chicks medicated starter, it will nullify the vaccine.
After you're fully prepared with living quarters for chicks and grown chickens, it's time to shop for chicks. If you aren't worried about finding specific breeds(and having them be accurate) you can go to any of your local feed stores and purchase what's available there. These will always be straight run(a mix of males and females) even if they claim they are sexed. If you aren't permitted to own a rooster in your area, I strongly suggest against this route. The best option is to order from a trusted hatchery. I am unaffiliated with any, but my favorite for over a decade is McMurray Hatchery. If you order chicks, your post office will call you when they arrive, and you'll get to go pick them up, which is my version of the perfect morning.
Once you get the chicks home, take them from their box one by one, dip their beaks in the water so they know where to find it.
After the chicks have been settled in, you'll know if your heat is too much or two little by their behavior. Huddling under the lamp in a cluster? Too cold. Chicks pressed against the walls of the brooder trying to escape the light? Way too hot. The sweet spot will be chicks spread out everywhere, eating and drinking. The heat will need adjusting weekly, gradually weaning them off. Once they are fully feathered and the weather is above 50F consistently overnight, they are ready to go outside permanently.
Once the chicks, now pullets(if female) are outside, eggs will come anywhere between 20 & 30 weeks, give or take on either side depending on breed. You can keep them on chick starter until they begin laying, and then change over to layer feed, with oyster shell supplement. The list of things chickens can eat is far greater than what they can't, and honestly we don't coddle them. Every. Single. Bit. of kitchen waste we produce goes into a bucket we keep in the kitchen. This bucket makes the rounds, from our worm bin, to the laying flock, to the piglets, to the breeder pigs, to the turkey coop. If it's fit for us to eat, it's fit for the animals producing more food for us to eat. Mow the lawn? Give them the clippings. Weed the garden or pick caterpillars off the cabbage? Chicken snacks. They're easy. Get going!