The Bible indicates Satan is a spiritual being or power -- that is, he doesn't have a physical body like we do. Any pictures of him, therefore, are simply the product of an artist's imagination (although they may hint at his evil nature).
At the same time, Satan can become visible from time to time -- just as God's angels can. (After all, the Bible says Satan was one of God's angels originally, before he rebelled and set himself up in opposition to God.) We don't know, however, what the devil looks like when he becomes visible; he can take various forms. When he came to Adam and Eve in the Garden of Eden he appeared as a serpent (see Genesis 3:1). Paul wrote that Satan sometimes "masquerades as an angel of light" in order to try to deceive us (2 Corinthians 11:14). Peter compared him to "a roaring lion looking for someone to devour" (1 Peter 5:8).
Never forget two important truths about the devil. First, he is real, and he is evil. His only goal is to oppose God in every way he can -- in the world, and in our lives. Don't treat him lightly, or think he's cute or cuddly. He is your enemy, and you should treat him the same way you'd treat a poisonous snake.
But you need to know a second truth: Satan is a defeated foe. By His death and resurrection, Jesus Christ overcame the powers of sin and death and Satan, and at the end of this present age that victory will be complete. Is your faith and hope in Christ?