Metaphor is a direct comparison, simile uses like or as, and personification gives human qualities to non-human things.
A metaphor is a direct comparison between two unlike things, without using words like or as. For example, Emily Dickinson's line 'Hope is the thing with feathers' compares hope to a bird.
A simile is a comparison using the words like or as. For example, the line from Bruce Snider's poem 'Chemistry' compares a rising feeling to a parakeet bursting from its cage.
Personification is when human qualities are given to non-human objects or animals. For example, the line 'the trees' branches reached towards the sun like arms' describes the branches as having human-like arms.