Sandor is wounded in the riverlands, and Arya leaves him there to die
But... is that it? What happens to him afterwards?
We find out what happened to Sandor "The Hound" Clegane in a Brienne chapter in A Feast for Crows. We are first served some clues, then told outright. First we see Sandor's horse, Stranger:
Then we see Sandor himself:
And later on, clues of the Elder Brother's involvement with Sandor:
We get confirmation that the Elder Brother has met Sandor:
The brother claims that "The Hound" is dead, but when reading between the lines, it is clear that what he means is that Sandor Clegane has left his violent persona behind him.
The Elder Brother then relates a story about himself being a knight, and being wounded on the Trident during the famous Battle of the Trident between Robert and Rhaegar, and finding his way to the Quiet Isle, where he found redemption. He finishes with:
It is clear that Sandor lives, when reading this chapter. One can only hope that he does not stay there for a decade, like the Elder Brother. My personal hope is that he is reunited with one of the main characters, and becomes their guardian, preferably Sansa. Others have theorized that he will become a champion of the Light, and fight UnGregor in Cersei's Trial by Combat. Whatever the outcome, it is sure to be interesting.
Sandor's fate has not yet been confirmed.
Spoilers from A Feast for Crows!
However, there is a pretty solid theory going around that Sandor is alive and is a novice (gravedigger) at the monastery on the Queit Isle. The evidence supporting this theory is as follows:
However, there is one quote by the Elder Brother that could go against this theory:
I personally do not believe we have seen the last of Sandor.
His westeros.org entry summarizes the answer for the books, whatever they will do with him in Season 5 of GoT, we will be able to watch next year, presumably.
As you state in your question, that is the position he is in at the end of A Storm of Swords, what happens to him afterwards (if anything) can be found in A Feast for Crows.