The Dark Arts
The Dark Arts differ from other forms of magic in the intent of the wizard using it. Most magic is relatively neutral--it can be used for bad or good. Some magic, however, is evil in its intention through and through. Spells of this kind are often called curses. Curses are spells that are often intended to cause harm to another person. This intention to do harm places that spell into the realm of the Dark Arts. However, simply casting a Curse spell doesn't mean that a person is using the Dark Arts. Ultimately, the deep, true intention of the caster is what makes the difference.
This is a difficult distinction to make in many cases. However, understanding the difference between acceptable and Dark magic is of key importance for witches and wizards in training, which is why Defence Against the Dark Arts is such an important class for students at Hogwarts. Some other schools have a reputation for teaching the Dark Arts, not simply Defence Against the Dark Arts; Durmstrang is such a school.
Dark Magic spells
Typical Dark Magic spells are called curses. There are offensive spells that shoot out of a wand like a gun; curse energy causes physical damage to things it hits besides the magical effect. Hexes and jinxes are lesser spells that adversely affect the target. As mentioned above, these spells are not necessarily Dark Magic. The intention of the caster is what actually makes the difference.
Dark Magic is more than simply curses, however. Magic that involves tampering with the free will of another person (e.g., the Imperius Curse), or which kills another person (e.g., Avada Kedavra) would be considered Dark Magic indeed. Voldemort spent years in magical research into ways of becoming immortal. This pursuit is also an example of Dark Magic, presumably because it tampers with the natural order of things.