How does the writer describe the sea in "The Most Dangerous Game"?

The sea is often described as menacing with figurative language.

Figurative language is a type of description that uses non-literal language.  The most common types of figurative language are simile, which is an indirect comparison saying something is like something else, metaphor, which is a direct comparison, and personification, which describes something nonhuman with human traits.

The story takes place on a Caribbean island, so there are plenty of times to mention the sea.  In the beginning, Rainsford is on a yacht passing by Ship-trap Island.

The sea is described with this simile.

"There was no breeze. The sea was as flat as a plate-glass window. We were drawing near the island then. What I felt was a--a mental chill; a sort of sudden dread."

This simile compares the sea to a big window.  It means that there are no waves on the sea because there is no breeze.  It adds to the creepy foreboding sense of the story at this point.

When Rainsford falls off the yacht into the ocean, personification is used to describe the sea.

Rainsford remembered the shots. They had come from the right, and doggedly he swam in that direction, swimming with slow, deliberate strokes, conserving his strength. For a seemingly endless time he fought the sea. He began to count his strokes; he could do possibly a hundred more and then—

When the sea is described as something you can fight, it underscores the struggle that Rainsford is facing.  As he is swimming, it is so difficult that it is almost as if the sea is fighting back.  Rainsford reinforces this when he refers to the sea as his enemy.

Personification or metaphor is also used to describe the sea lapping on the shore. 

His eyes made out the shadowy outlines of a palatial chateau; it was set on a high bluff, and on three sides of it cliffs dived down to where the sea licked greedy lips in the shadows.

Either animals or people can have lips, so the comparison is not necessarily personification.  It is figurative though, because obviously the sea cannot actual lick.  The description adds to the menacing characterization of the sea.