How can you differentiate between a simile and a metaphor?

The definition of a metaphor is...

...an implied analogy or unstated comparison which imaginatively identifies one thing with another.

In other words, two dissimilar things are being compared as if they were the same, however what they share are simply the same characteristics, and "like" or "as" are NOT used in the comparison. I was once told to think of a metaphor as X is Y. You may recall the famous song lyrics:

You are the sunshine of my life.

"You" is X and "sunshine" is Y. "You" is not literally "sunshine," but "you" may have the same characteristics of the sun: being warm, brightening up one's day, helping someone find his or her way in a troubling time, etc., as the sun aids us in navigating throughout our world each day. The subject of the song ("you") is not hot to the touch or too bright to look at without sunglasses. And while the reader may not know "you," he or she can imagine what the subject is like in bringing to mind the positive characteristics of the sun.

Robert Herrick uses a metaphor in his poem, "To the Virgins, to Make Much of Time."

The glorious Lamp of Heaven, the Sun,

The higher he’s a getting... (5-6)

Herrick is saying that the sun is a lamp in the heavens. (X is Y.) A metaphor, as you can see, is a figure of speech—also called "figurative language;" it should not be taken literally. Figurative language is commonly used in poetry: metaphors are very popular with many poets.

The simile is defined as...

...a figure of speech in which two things, essentially different but thought to be alike in one or more respects, are compared using “like,” “as,” “as if,” or “such”...

In other words, a simile is a figure of speech that compares two dissimilar things that share the same characteristics, using "like" or "as." Using an equation as shown above, a simile can be represented by X is like Y. Lyrics from another old song are, "She's like the wind." First, two things are being compared. "She" and "the wind." It is not to be taken literally: she cannot sweep along invisibly through a meadow, blow over trees or howl on a winter night. However, she may be hard to contain or keep in one place; she may be free and unhindered. Secondly, "like" is used. However, one must be careful when identifying a simile—just because one sees "like" in a sentence does not mean it is a simile. "I like ice cream" makes no comparison, and "like" is used as a verb.

Samuel Taylor Coleridge's The Rime of the Ancient Mariner is loaded with figurative language, including the simile below:

The selfsame moment I could pray;

And from my neck so free

The Albatross fell off, and sank

Like lead into the sea. (285-288)

In this example, the speed with which the dead bird (the albatross) sinks into the ocean is compared to the sinking of lead into water: it happens very quickly. The reader is not there to see the bird drop into the water and immediately disappear from sight, but generally one can imagine how quickly a piece of lead drops and disappears in water.

Metaphors and similes allow a writer to make his or her descriptions much clearer, bringing images of great clarity into the reader's mind.