Step 1: learn what the laws in your area are. I'd hate to have you buy a dozen chickens only to get cited for going over the legal limit! My city allows up to 6 chickens on a residential lot depending on square footage. We have just enough space to legally own 6. I have a lot of neighbors who own more and haven't been caught by the chicken police. While I would never (publicly) promote that, you probably wont have a problem if all your neighbors like you. Also, most cities don't allow roosters (dogs that bark incessantly at 3am, however, are usually permitted).
Step 2: decide how many chickens you want. If you're getting them for eggs, you'll probably want a breed that lays close to daily. Chickens are social, so you should plan on at least 2. So now the question remains, do you want 2 dozen eggs a week, or more?
Step 3: build a coop to fit your number of hens. Please, please, please don't put this off until the day before you get your birds! It takes a while to build one (unless you want to pay gobs of money for one already built - and you may want to consider that). There are a lot of styles to choose from. Just google "chicken coop plans" and you'll see there are lots to choose from. If you're handy, you can probably figure it out from pictures. If not, just buy the plans and save yourself the headache. I have 2 coops since I don't make decisions well. I have a permanent structure that has been moved 3 times (it's hard to find a spot that gets sun in winter and shade in summer!) and a movable tractor called a chicken ark as well.
Isn't that great!? It's not mine, but I copied it.The permanent coop will hold 6 birds. They say to plan on 2-4sqft/bird. Mine is 20sqft inside + 2 nesting boxes. The run is larger, 4-5 sqft/ bird. The run is the open outside area next to the coop.
Once I finish the run remodel -when the weather warms a bit more) I'll post pictures of mine.
Step 4: look around for chickens!! I use KSL, a local internet classifieds. March/ April is a great time to buy chicks at your local farm supply store, but chicks require more time and equipment. You need a breeder box (an old tote will work for this), heat lamp, special food, a special food tray and waterer, and a place inside to put them. I have no garage and the laundry room is also the bath, so chicks are not an option for us right now. When looking for birds you want to get pullets (teenage hens) or year or less old, generally. Plan on them laying for about 2 years.
Some people have difficulty mixing breeds (chickens can be racist), but many are just fine, especially if you get them from the same place and they're younger.
Be sure to check their living conditions. Mine were not provided a roost from their previous owner, which I didn't think would be a big deal. But it's taken MONTHS to teach them to sleep on the roost so they aren't pooping/sleeping in the nesting boxes.
Step 5: enjoy your chickens!! Check on them throughout the days until you both feel established. Then simply check their water and food daily and enjoy your delicious eggs!