There are 3 Basic ways to get started with chicks. You can order eggs, and incubate and hatch them yourself, you can order day old chicks, or you can let it happen naturally. I'm going to go over all of these methods with some pros and cons.
Order Eggs
To hatch your own eggs, you will need some equipment, and a lot of patience. I order my eggs and chicks from Meyer Hatchery. This is the cheapest method to buy the actual chickens. Each egg is about $3. You cannot buy grocery store eggs and hatch them - the eggs need to be fertilized.
You will need an incubator to keep the eggs warm, and in a moist enough environment. Meyer Hatchery is really great they provide you with instructions on temperature and humidity levels that the eggs need to stay at. I highly recommend getting an incubator with an automatic egg turner. If not, you will need to mark your eggs (carefully) and rotate them several times a day. Chicken eggs are in the incubator for 21 days. Day 18 is when "lock down begins" You lock the incubator, and Do NOT open it again until ALL the eggs have hatched.
I did not follow directions on this and was so excited to see my new little hatchling, and opening the incubator killed all the other chicks. Lock down is serious. The little chicks should stay in the incubator until they are all dried off and can stay there without food or water for 2 whole days. Be patient, give it time, let them all hatch.
Pros:
Eggs are cheaper than buying chickens
You get to see the chicks be born
Cons:
It's a little tricky
Not all chicks may hatch
You have to buy the start-up equipment
You do not know if you are getting hens or roosters
Day Old Chicks
You can decide to order day old chicks. For this I also use Meyer Hatchery. Day old chicks can get expensive if you start getting particular about the breed, and cost anywhere from $5 - $40 per chick.
You need to buy a minimum of 3 chicks, and they get shipped to you via mail. You can also buy chicks at many local stores and come directly home with them. In my experience the sexing at the local stores is not as accurate as from a hatchery, but all my chicks survive the trip home. Not all chicks survive the mail order shipping. Meyer is very good about sending replacement chicks or refunding you for any that did not make the journey. Once you receive your baby chicks (or once your incubated chicks hatch) you will need to place them in a brooder with a heat lamp, until they have all of their feathers (and not the chick down). Once they have their feathers, they can go into the Coop.
Pros:
You can choose if you want hens or roosters
Pretty straight forward, and uncomplicated
instantly have baby chicks - no waiting
Cons:
Not all chicks survive the mailing
Most expensive of the 3 options
Natural Method
If you already have a flock with roosters, you can let nature take its course. It is likely that all of the hens are bred every day by the rooster, so most if not all of your eggs will be fertilized. You can take your own fertilized eggs and put them in an incubator. Or if you are lucky, one of your hens will go broody. When a hen goes broody, she stops laying eggs and will sit on a pile of eggs for 21 days without leaving (except to
occasionally get a bite to eat and a quick drink of water). Broodiness can also be contagious, once one hen starts a few others may follow in suite. In this case, just leave them be. Let them sit on the eggs until they hatch. The momma hen will keep the babies warm, and teach them how to eat, and become part of the flock.
Pros:
Cheapest method, as in totally free
Hands off - You don't have to do anything. Mama has this handled.
It gives your hens the chance to be a mother
Baby chicks can be directly integrated into the flock, no brooder required.
Cons:
You have no idea how many chicks you are going to get. (40 eggs does not equal 40 chicks. it may equal 6 chicks)
You have a 50/50 chance of getting hens and roosters
Not all babies are accepted by the flock, and some may be killed.