First, I'll give a brief description of spell types¹ :
Spell: The generic term for a piece of magic.
Charm: Does not fundamentally alter the properties of the subject of the spell, but adds, or changes, properties. Turning a teacup into a rat would be a spell, whereas making a teacup dance would be a charm. The grey area comes with things like 'Stunning Spells', which on balance I think are Charms, but which I call spells for alliterative effect.
Hexes: Has a connotation of dark magic, as do jinxes, but of a minor sort. I see 'hex' as slightly worse. I usually use 'jinx' for spells whose effects are irritating but amusing.
Curses: Reserved for the worst kinds of dark magic.
J.K. Rowling's Personal Website
So that's a basic linear explanation of the different levels of magic.
One characteristic of Dark Magic is that it does not seem to be able to be healed or counteracted. This is obviously true of Avada Kedavra and extensive damage done by the Cruciatus Curse. The Imperius Curse is a little more interesting -- a person can develop the skills necessary to resist the Imperius Curse, which Harry shows the proclivity toward in Goblet of Fire when Barty Crouch Jr. as Mad-Eye Moody was teaching DADA. Sectumsempra is an example of a curse that is Dark Magic -- and it seems a bit murky here, because Snape healed Malfoy of Sectumsempra in Half-Blood Prince -- when Snape curses George Weasley's ear off in Deathly Hallows, Molly says:
"I can't make it grow back, not when it's been removed by Dark Magic. But it could have been so much worse. . . . He's alive."
Deathly Hallows - page 73 - US Hardcover
There are numerous instances in canon of non-treatable injuries and death caused by Dark Magic: Dumbledore's injured, blackened hand; Moody's missing eye, leg, and the chunk out of his nose; the Longbottoms torture to the point where they lose their minds; Lockhart's backfired memory charm (I would argue this as possible Dark Magic due to the malicious intent behind the spell when Lockhart cast it); lycanthropy; the Horcrux potion in the sea cave that Dumbledore drank; the Dementor's Kiss; Cedric Diggory's murder; Broderick Bode's murder in St. Mungo's via Venomous Tentacula; Bathilda Bagshot's murder (means unknown, but it seems likely either Nagini killed Bathilda or a Death Eater or Voldemort did with Avada Kedavra); Quirrell via possession by Voldemort; Peter Pettigrew strangled by his silver hand for showing Harry a scintilla of mercy; etc.
It seems that magic gives off traces -- either good or bad -- that can be detected by a skilled witch or wizard.
"Magic always leaves traces," said Dumbledore, as the boat hit the bank with a gentle bump, "sometimes very distinctive traces. I taught Tom Riddle. I know his style."
*Half-Blood Prince - page 563 - US Hardcover
If Dumbledore is able to discern Tom Riddle's style of magic just from the traces left at the sea cave -- and I think it's fair to say that Tom Riddle's style of magic would be Dark -- would it be plausible to extrapolate that all witches and wizards leave a "signature" of sorts when casting magic, that is unique to them? And if one know the witch or wizard in question, might they be able to tell the intentions of the person who cast a spell? For example, if the imprint of Wingardium Leviosa were detected, the motivation behind the spell might vary if one compared Harry Potter to Lucius Malfoy. The former might have been lifting cupcakes for Crabbe and Goyle to find ala Chamber of Secrets, and the latter might have been casting Wingardium Leviosa for the purpose of frightening and torturing Muggles ala Goblet of Fire.
Also, again, I think intent has something to do with the essence of Dark Magic. I'll give some examples that are not necessarily reflective of my personal ethics, but can be food for thought.
Harry and Ron used the Imperius Curse inside Gringotts on the Death Eater Travers, in order to preserve their cover and to successfully find and take the Hufflepuff Cup Horcrux. While technically an Unforgivable, was this curse performed in the spirit of acting for the greater good? Is this Dark Magic?
Voldemort indiscriminately kills Goblins and some of his Death Eaters when he learns the cup Horcrux has been taken from the Lestrange's vault. What was the motivation behind Voldemort using Avada Kedavra in this situation? Nothing but pure unadulterated anger. Is this Dark Magic?
Avada Kedavra is always classified as Dark Magic -- yet, Horcruxes aside, how many would have minded if Harry (or anyone, for that matter) had used Avada Kedavra to kill Voldemort? Would that be Dark Magic? What about when Snape used Avada Kedavra on Dumbledore? Was it murder (with the specific intent to commit a homicide) or was it an act of supreme mercy? Was Snape's killing of Dumbledore Dark Magic?
Sectumsempra would probably be classified as Dark Magic. Is Harry's use of Sectumsempra against Malfoy in Half-Blood Prince justified? Was it Dark Magic? Was Snape's use of Sectumsempra against James Potter in chapter 28, Snape's Worst Memory, in Order of the Phoenix justified, after James's brutal bullying of Snape? Hmm. I'm not saying it was right, but I can empathise with the motivation behind Snape using Sectumsempra in that instance².
I think good intentions gone horribly wrong also have to be taken into consideration. For example, Lily and James Potter, a Sirius Black's urging, changed their Secret Keeper from Sirius to Peter Pettigrew, thinking it would be less obvious to Voldemort. Obviously, the Potters did not know that by this time Peter was a Death Eater and ultimately their lives were lost because of Peter's betrayal of the Fidelius Charm. Fidelius is but a charm, yet it had the worst possible consequences for the Potters when its parameters were violated.
The questions asks what discerns Dark Magic from regular magic, and my answer is that it depends, but it's recognisable when it occurs.
¹I was writing this as the other question came up asking the differences between spells, hexes, enchantments, and curses. Hence the repeated information.
² I realize the spell Snape uses against James is not specifically named as Sectumsempra, but it is implied by the nature of the spell.