By their morphology
Crickets and katydids
Crickets, katydids, and grasshoppers belong to the order Orthoptera. Some authors include walking sticks, cockroaches, and mantids, but we place them in other orders. Orthoptera, as we restrict it, is divided into two suborders: Caelifera (grasshoppers and relatives) and Ensifera (crickets, katydids, and gryllacridoids).
The Caelifera have antennae that are shorter than the body and short ovipositors. Those species that make easily heard noises usually do so by rubbing the hind femurs against the forewings or abdomen or by snapping the wings in flight. Tympana, if present, are on the sides of the first abdominal segment.
Ensiferans, with the exception of mole crickets, have antennae at least as long as their bodies. Ovipositors are usually long and blade- or needle-like. Species that produce calling songs nearly always do so by rubbing the forewings together. Those that hear have the ears in their foretibiae.
Cicadas belong to the order (or suborder) Homoptera, which is characterized by piercing sucking mouthparts and, in most winged members, membranous wings held rooflike over the body. Most cicadas are more than 20 mm in length (from head to tip of membranous forewings at rest). All have three ocelli and the antennae arise between rather than beneath the eyes.
The upper three images are adults of representative species of North American cicadas. They vary in length, color patterns, and habitat. The lower image is of a cicada nymph.
By their songs
We may eventually attempt to make it easy for someone to identify the most commonly heard species of singing insects by their songs alone. For now, we will only give these guidelines for deciding what major group of singing insects is likely responsible for a particular call you hear:
Crickets songs are musical to the human ear because their carrier frequencies are relatively pure and low.
Katydids and cicadas songs sound buzzy, raspy, or whiney, because their carrier frequencies are less pure and are higher than those of crickets. Cicadas call almost exclusively during daylight hours and at dusk, usually from trees and shrubs, whereas most katydids call only at night and many are not resticted to woody vegetation.