Here are some of the figures of speech there is.
Metaphor is direct comparison therefore it makes comparison with the absence of "as" and "like". In the statement, "He was boiling mad!", a person's anger is compared to that of a boiling pot which gives off steam, overflows and is very hot.
To personify a thing, an idea or even an animal is to give it an attribute - skill, personality, behavior, etc. - of a human being. In the statement, "The moon's shadow danced on the lake.", shows a picture of the moon's shadow on the surface of the lake moving in the direction the wind moves the water to.
Hyperbole is plainly exaggerating an event, condition or circumstance. In the statement, "I am so hungry I could eat a horse.", the speaker simply means he is very hungry but it doesn't mean he'd eat a horse.
Irony usually says the opposite of what it actually means. In the statement, "Your family doctor was as kind-hearted as a wolf.", the speaker actually means the doctor was rude. That is actually sarcasm, a style mostly found in ironic statements.
Onomatopoeia is perhaps the easiest to recognize, that of course if you are familiar with the sounds around you. In the statement, "He went on buzzing so I left." The word "buzzing" refers to the sound bees make. The speaker expresses annoyance of such sound that made him leave but this doesn't mean there are bees in the vicinity where he was.
You can also check out 13 figures of speech I discussed in this video: