Don't get in over your head.  You can't raise them all!  Stick with one or two caterpillars.  The best caterpillars for kids to raise is a Monarch or a Black Swallowtail.  Unless you have LOTS of milkweed to feed the Monarch caterpillars, stick to the Black Swallowtail.  They eat a more common plant that's more easily acquired.

Monarchs will only eat plants in the Milkweed family.  There are over 100 varieties available, and grow in many wild places throughout the US.  Monarch cats are big eaters and poopers.  The chrysalis is really pretty, and you can tell before the butterfly emerges, because the skin of the chrysalis will become clear, and you can see the wing markings through it.

Black Swallowtail caterpillars eat plants in the Umbellifer family.  This includes parsley, dill, fennel, even carrots (the green tops).  If you don't have these plants in an herb garden, you can easily go to the nursery and buy these herbs.  This caterpillar is really cool - it has a 'scent horn' that sticks out of its head when disturbed.  They are eating, pooping machines (like most other caterpillars.)  The chrysalis will be either green or brown, depending on the conditions where it pupates.  It, too, will become transparent just before the butterfly emerges.

You can use plastic 'critter holders' or aquariums.  I buy mine at Walmart, from the fish/hamster dept.  You can also use a large plastic container, with a big hole cut in the top for air.  Put a piece of nylon screening under the lid so the caterpillars won't escape.  Make sure your container is large enough to hold plenty of food and the cats.  You must clean it out EVERY day, get rid of the poop and old food.   Give them fresh food daily (maybe even 2 or 3 times.)

If the container is tall enough, you can set a small potted plant in the container and let the caterpillars eat directly from the plant.  Or you can clip leaves or branches off the plant and place them inside.  You can also use a small bowl (like a butter bowl), place wet sand inside and put the lid back on.  Poke holes in the lid, big enough to put stems through into the wet sand.  This will keep your parsley or milkweed clippings fresh, allowing them to stand up in the container.  You can probably get a better look at the caterpillars this way.

Your caterpillar will take about 10 - 14 days to turn into a chrysalis (from the day it hatches).  It will shed its skin (molt) several times during these days.  The times between molts is called an 'instar'.  Often the caterpillar will change its look after molting.  A baby Black Swallowtail caterpillar is black with a white 'saddle', but the big one is green, white, and yellow.   The Swallowtail will 'clean its guts' just before it readies for the next stage in life.  You'll see a big, yucky, poopy mess in the bottom of the container, and it will stop eating, and start wondering around, looking for a place to pupate.

You will need to provide your caterpillar the proper place to 'hang out' as a chrysalis, and different species have different needs.  A Monarch will hang in a "J" position for a day before shedding its skin for the last time.  It needs a place near the top of the cage, so that it has enough room to hang upside down.  They usually hang from the netting on top of the cage.  A Black Swallowtail will lean back after spinning a 'girdle' around its midsection.  Its feet will be stuck in a silk pad, and this along with the girdle will hold it in place.  A slanting twig or stick will work for the Black Swallowtail.

After molting for the last time, they will stay in the chrysalis form for 10-14 days.  If you disturb the Black Swallowtail chrysalis, it will move its tail in an attempt to scare you away.  The Monarch chrysalis is a beautiful green jewel, with gold specks decorating it.  The Black Swallowtail chrysalis will either be brown or green, and will blend in with its surroundings.

About a day before emergence, you'll see a wonderful change in the chrysalis.   They will become transparent, as the pigmentation begins to appear in the pupal skin.  You can see the wing patterns through the skin!  Normally, most butterflies emerge early in the morning, between 5:00 and 10:00.  This will be your best bet to watch as the butterfly emerges.  It's almost like it crawls out of bed from a long sleep.  It's wings will be very small and rumpled, but as it hangs and dries, the wings will stretch out and look normal. 

When the sun is out, and your butterfly is more active, it's time to release it!  If you just put your finger directly in front of its face, along the container, it will usually crawl onto your finger.  Sometimes it will fly off the finger soon as its clear of the container, or you can put it right up next to a flower, and it will crawl onto it.  Put it in a good, sunny spot.

PARENTS:  Never allow a child to raise a stinging caterpillar!  "Safe" caterpillars include Sulphurs, Painted Ladies, Swallowtails, Gulf Fritillaries, or most butterflies.  It's usually the moth caterpillars that sting.  Caterpillars are delicate creatures, too much (or rough) handling can kill them or damage internal organs.  Don't disturb caterpillars preparing to pupate, do not UNDER ANY CIRCUMSTANCE attempt to move it!!!   Once it's attached itself, leave it alone.  If you gather one from the wild, instead of picking the caterpillar from the plant, clip the twig its on, and place the whole twig in the container, allowing it to crawl on its own to the new food.