"These pictures ...give a fair representation of what happens to those who suffer, for instance, the Cruciatus Curse ... feel the Dementor's Kiss ...or provoke the aggression of the Inferius."
-- Severus Snape (HBP9)
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. These spells are not necessarily Dark Magic, however. The intention of the caster is what actually makes the difference. For instance, Snape told Harry that Sectumsempra was a Dark spell when the boy used some foolish wand-waving that cut up Draco until he nearly bled to death (HBP24). But Snape used the spell defensively during the Battle of the Seven Potters to keep a Death Eater from killing Remus Lupin and George Weasley, although in doing so he accidentally amputated George’s ear (DH5,DH33).
Dark Magic is more than simply curses. 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.
History and Notes
Some of the most famous (infamous?) creators and practicers of Dark Magic include Herpo the Foul who created the first Horcrux, Ekrizdis who captured and tortured Muggle sailors, and Merwyn the Malicious who created many evil spells.