When your quail chicks hatch from their shell they will need to be kept in a brooder for about a month or so. A brooder is simply a heated cage.
Brooder Cage
I use a large plastic storage container like this for my brooder.

It’s cheap, easy to clean (just hose it out) and easy to move around. You can also use a cardboard box, a cooler, an aquarium, a plywood box, etc. Anything that will keep the chicks contained is fine.
Heat
Quail chicks don’t hatch with full feathers so you’ll need to keep them warm. To heat the brooder, the simplest way is to use a standard heat lamp like this.

I use a red 250 watt bulb in the lamp like this.

One word of caution: be sure that you use an outlet and electrical cords that are rated for the heat lamp. You don’t want to be flipping breakers or starting any fires.
Just clamp the heat lamp so that it shines into one side of the brooder and leave it on 24 hours a day. You want the temperature in there to be about 99 deg F to start with. Raise or lower the lamp to get the temperature about right. It doesn’t have to be exactly 99 deg F. The chicks will self regulate and move away from the light if they are too hot and will clump all together right under it if they are cold. This is why it’s a good idea to put the lamp to one side of the brooder and not right in the center.
If you see all the chicks bunched together beneath the light they are a little chilly, so just lower the lamp a little to increase the temperature. And if they are all hanging out on the far side of the brooder away from the light they are a bit warm, so raise the lamp a little to cool them off a bit.
You want to gradually lower the temperature in the brooder until they are all feathered out and ready to be moved to their grow out cages. Do this by raising the heat lamp about a foot higher every week or so. After about 4 weeks, your chicks should be ready to move into their new digs in the grow out cages with plenty of feathers to keep them warm.
Bedding
Bedding is easy for the quail chicks. I use paper towels. They are cheap, absorbent and I just toss them in the compost pile when they need to be changed out.
Other things can be used for bedding as well, but be sure that it is not slippery like newspaper. Don’t use newspaper! The chicks are really unsteady on their feet when they first come out and they could develop foot and leg problems if they don’t have a good non-slip surface that they can learn to walk on.
Water
This is a really important one. Use standard chick waterers like these.

The important thing to remember here is that you need to put marbles, pebbles, or something in the tray of the waterer for the first few days to prevent the chicks from falling in and drowning. Again, the quail chicks are really clumsy at first and they can and will fall in and drown.
I use marbles that I had laying around. The chicks can poke their beaks in between the marbles and get the water just fine. And if they get on top of the marbles they won’t drown.
They will muck the water up, so change it out often so they have a fresh supply.
Feed
I use the same feed for coturnix quail from the day they hatch to the day they are dispatched to the freezer: MannaPro Gamebird/Showbird Crumbles.


For the first few days I crush the crumbles up so they are more easily eaten by the chicks, but this probably isn’t necessary. There’s plenty of small bits in the crumbles for them. But it you want to you can use an old coffee grinder, a mortar and pestle or a rolling pin to crush it up. Until the chicks are steady on their feet I simply pour a small pile of the feed on the floor of the brooder and let them go at it. They will toss it around and play in it, but it’s easy for them to get at it that way.
When they can walk around pretty well I use a standard chick feeder like this and stop grinding up the crumbles.

There’s no need to ration the feed at all. Have them eat as much as possible! They grow so fast it’s remarkable, so free access to food and water is important.