I help maintain a colony of Manduca sexta in a lab and animals are required at specific stages each day, so it's necessary to collect eggs daily from a cage where adults are allowed to fly around, feed from a container of sucrose solution, and lay eggs on a tobacco leaf. You can use leaves from almost any plant in the nightshade family, Solanaceae to get them to oviposit. Some examples are nightshade, datura, brugmansia, potato, and tomato. We prefer to use tobacco because we grow a perennial variety, the leaves are large, and eggs are easily collected by gently rolling them off the fuzzy leaves. The leaves need the ends to be cut under water to maintain the leaves' ability to channel water as air bubbles are made in the initial cut off the plant. The leaves also need to be kept in a jar of water to make sure they remain fresh and enticing for the female moths that use chemical cues to determine where to oviposit. The sucrose solution in the cage should have a lid with a wick from which they'll drink from, and must be checked every couple days by smell to ensure that it has not fermented.
The eggs hatch in 3 days and hatchlings grow very quickly in an incubator set at 27 degrees Celsius with lights on a long day setting to prevent them from developing into diapausing pupae. We feed them with a wheat germ-based diet made for gypsy moths and each caterpillar is kept separately due to the fact that they are rather aggressive towards each other if they start crawling onto one another. It's not unusual to find individuals bleeding and dying if they've been overcrowded. Starving them results in self-mutilation in the form of eating their own horns to a stump or cannibalism if more than one is kept together.
At 27 degrees Celsius, they go from hatchlings to wandering, or the pre-pupal caterpillar stage, in about 20 days, but may take longer if they are left without food or if they are feeding on spoiled food for more than a day. Poor conditions can extend the larval stage considerably and will end in dead caterpillars if not rectified. The wanderers are placed into wooden blocks with holes drilled to be slightly greater in diameter than the caterpillars and then the side of the block with holes is blocked off to allow the wanderers to feel like they've gone underground and found a place to pupate. After 17 days, they are removed from the blocks as pupae and the pupae are usually a minimum of a day away from eclosing to a maximum of a week away from eclosing depending on when the caterpillars pupated within the blocks.
The pupae are exposed to long day lighting conditions out of the blocks for a day before being placed into the adult cage where they will emerge and reproduce. Any pupae that have begun to show signs of preparing to eclose are immediately placed in the adult cage. Signs of imminent eclosion are living pupae that have developed a dark coloration. As they approach eclosion, the exoskeleton of the pupae will grow thinner and the pupae will become soft and you will be able to see the markings on the moth within. The cage must have grippable surfaces so that the emerging moths can hang themselves and properly dry their wings--any that have not had the opportunity to position themselves for proper wing expansion and drying will be unable to fly and end up being unable to feed and lay eggs on the leaf.
Breeding isn't difficult, but maintaining a colony in order to continue to have animals is a lot of work and requires a great deal of room and food. A very important thing to remember when using artificial diet is to feed enough that they'll have food to eat for a day, but feed sparingly so that you don't overfeed and waste food through spoilage. Spoiled artificial diet becomes a breeding ground for bacteria that can sicken your caterpillars and the food itself rapidly loses nutrional value as it spoils. Rearing them in individual cups will keep them feeding instead of fighting over space and it'll help you more accurately determine how much food to give them as they grow. You cannot sex larvae, so you'll always need to set aside enough individuals to ensure that you have both males and females.