Taking Care of New Chicks
There isn't anything much cuter than a new born baby chick...a little fluff ball that fits in your hand and make tiny little peeping noises. Although baby chicks have some basic needs, and are a bit fragile (as most babies are), with little effort, you can successfully raise your chicks into full grown birds--whether you want them for pets, eggs, meat or a combination.

Bringing the babies home...
Okay, so maybe you've learned that your city will allow you to have 3 hens (no roosters), and the chicken coop has to be at least 100 feet away from your neighbors house. You've calculated how big your hen house and chicken run need to be in order to accomodate your new chickens. You've built (or bought) that coop. You've decided what kinds of chickens you'd like to raise...and you're ready to head off to the feedstore!
(If the above paragraph isn't true yet, head over to Before You Buy New Chicks first.)
The other stuff you'll need...
First, you need a place to keep them. For the first 6-8 weeks of your new chicks lives, they need to live with you. Yep, that's right. They're temporary indoor pets. A perfect way to house them for these initial weeks is in a big box (get a free appliance box from a home improvement store), an extra large plastic bin (with a screen over the top--especially if you have other indoor pets roaming around that might like nibble on the new little babies) or a large sized dog crate (see pictures below).
Line the bottom of your box with cedar shavings. Change the shavings occassionally to keep the area clean (and the smell down).
You'll also need a heat lamp. Remember, these chicks are usually only 1 day old when they get sent to the feed store. It's important to keep them warm.Hang the heat lamp over the box where your chicks are. Adjust the height of the light depending on if your chicks are still too cold (they're huddled together), or too hot (they're spread out as far away from the lamp as they can get).
Your new babies will need clean water and food at all times. Be careful, especially with the water...don't give them water in something too deep...you don't want them to drown.

Poop happens.
If you keep your new chicks warm, fed and watered, you're off to a good start. The only other major thing you need to watch for is their backside--make sure that it doesn't get clogged with poop (and stop up your chick which will kill it). If this happens, the solution is a simple one: Take a warm, wet cloth and gently remove the poop caked on your chick.
TLC
Handling your chicks will help them grow up to be tame pets. Handle them often, but don't forget to watch your hands BEFORE (to protect them from your germs) and AFTER (to protect you from their germs). Most chickens, by nature, are gentle creatures. Get them used to being handled early and they'll grow into tame, wonderful animals.

More information that might interest you:
Before you Buy Baby Chickens
Taking Care of Baby Chicks
Getting Started with Chickens
Chicken Raising and Care
Basic Chicken Coop 101 and Basic Chicken Coop 102
Free Chicken Coop Plans
How to Make an Automatic Chicken Waterer
Weird Chicken Facts