Ms. Grasshopper goes to a lot of trouble to lay her eggs either in the ground or in a soft layer of rotting wood. That way they are protected from the weather and can sleep safely through the winter. The tail end of her body has a special attachment to dig a suitable hole and to tuck the precious eggs safely inside it. It is called an ovipositor, which means an egg placer.
The eggs are small flat ovals, pasty white or pale grey. The female lays a cluster of perhaps 100 of them at one time. The cluster is packaged and stuck together inside her body. It comes out in a nest pod. The ovipositor pushes it down into the soil sad adds more sticky material to seal out the moisture. Chances are, the eggs will sleep soundly until spring. Then they hatch into mini grasshoppers. As they grow, they shed their skins four or five times. After the last molt, they come forth with grasshopper wings.