Depending on the plant, insect-eating plants use several mechanisms to capture their prey: pits to fall into; sticky flypaper-type sections; snap traps; vacuum suction; and inward-pointing hairs that operate like a lobster trap.
There are hundreds of types of insect-eating plants but these are among the most commonly grown by gardeners. Never collect them from the wild; many are on protected or endangered species lists. Always check the source of your nursery's plants.