The best way to learn about an insect's life cycle is to watch it first hand.
A really easy and amazing insect to care for is a butterfly.
We used the kit by Insect Lore and love it:
You receive a net habitat and a cup of caterpillars with food. Once the caterpillars form their chrysalis you transfer them to the net.
Our butterfly emerging from it's chrysalis
Butterflies grazing on juicy oranges
Butterflies mating!!! We did not expect to see this.
Butterfly laying over 70 eggs.
The instructions said to let the butterflies go within a week and we should not have to worry about eggs. These eggs appeared 5 days after the butterflies emerged.
If you look closely, there is a tiny and very hungry caterpillar on top of this leaf.
We let most of the eggs out in a field in upstate NY and kept a few at home on a bed of wet paper towels and leaves.
And of course we had to introduce him to the famous hungry caterpillar by Eric Carle (in Hebrew).
There are tons of other activities that can be down alongside "The Very Hungry Caterpillar":