Insects are characterised by having six legs. Of course there are exceptions: many larvae have no or additional legs (but these are stumpy and obviously different); some adults, especially parasitic forms, have reduced legs. Finally not everything with six legs is an insect: juvenile mites and copepods are both six-legged.
Insects have a chitin exoskeleton. Because this is impermeable to gases, they have a system of branching internal breathing tubes (trachaea) connecting to the outside through paired openings (spiracles) on each segment (generally). Because the exoskeleton is stiff, it is shed (ecdysis) regularly during growth; the number of moults is usually constant for a given species, and the stages between are called instars.
Insects are the most species-rich group of organisms on the planet.
Diagnostic features
Almost all insects have six-legs, at least when adult.
Almost all organisms with six legs are insects - the exceptions are very tiny, although spiders and harvestmen can lose two legs, so care needs to be taken.
Any cold-blooded organism with wings (ie not bird or bat) is an insect.
Curation
Hard-bodied insects are generally pinned (the exception being beetles which are usually carded, and very small species.) Either way they often need to be relaxed after killing, unless you catch them just right.
Soft-bodied species and larvae are best preserved specimen tubes in 90% alcohol. Use tubes with flat sealing caps ("alcohol tubes") rather than the 3-finned caps which aren't vapour-proof. To reduce evaporation, store the tubes in a sealed jar (jam jar or kilner jar) which itself contains a few cm of alcohol.
Lab. techniques
RELAXING Insects are best relaxed in a jar with a few drops of vinegar on a piece of kitchen towel in the bottom. Use a squat jar such as those sold containing savoury spreads. Small insects will relax overnight, larger or stiffer ones might require a couple of days. Beware that the acetic acid will turn copper or brass-headed pins green.
MICROSCOPE PREPS Insects or insect parts can be softened in 10% KOH. This generally means heating in a water bath for 5 or 10 minutes (depending on size) or leaving overnight at room temperature.
This is the usual method of preparing microscope slides, eg for genitalia preps.