How do butterflies communicate? Is it like honeybees?

Butterflies do not communicate like honeybees but they use some of the same kinds of communication. Butterflies can communicate with each other (same or different species) by color, chemicals, sound, and physical actions.

Color patterns are used to signal their sex or species to each other.

Chemical pheromones are used by both sexes of some butterflies to attract the opposite sex or to signal species identity in courtship. A few butterflies make clicking sounds (males of genus Hamadryas) to protect their space.

Some chrysalides (Gossamer-wing butterflies) make clicking sounds to attract ants that in turn protect them.

Physical actions such as aggressive flight or postures are used in courtship or to protect resources such as an important flower.

Caterpillars of some species produce sugary substances for ants which in turn protect the caterpillars.

Whole books have been written on this topics. This is a brief, simple answer.