Avada Kedavra's a curse that needs a powerful bit of magic behind it — you could all get your wands out and point them at me and say the words, and I doubt I'd get so much as a nosebleed.
When wizards graduate from Hogwarts, would they be skilled enough to perform these curses? Or would they still need training in the Dark Arts that Hogwarts doesn't teach?
Mad-Eye Moody (actually Barty Crouch Jr. using Polyjuice Potion) says that the students in his class could all attempt the Killing Curse on him and he'd remain unharmed.
“Avada Kedavra’s a curse that needs a powerful bit of magic behind it – you could all get your wands out now and point them at me and say the words, and I doubt I’d get so much as a nose-bleed. But that doesn’t matter. I’m not here to teach you how to do it.”
- Harry Potter and the Goblet of Fire, Chapter 14 (The Unforgivable Curses)
That he's willing to tell a class of teenagers that they could all cast it on him, likely knowing the possibility at least one of them might, that he phrases it as 'a curse that needs a powerful bit of magic behind it' seems to imply that there is a skill component to it. Teenagers in general are prone to extreme emotions, including anger and hatred. If it was simply emotional he might have been a bit more wary of the possibility that one of his students might truly hate their teacher enough to kill them. Teenagers are capable of extreme hate and anger, including actually wanting people to die, or wanting to kill them. In addition, they're impulsive - they might not consider the consequences of casting an Unforgivable Curse before attempting it. We know the wizard casting them doesn't have to be 'evil' since McGonagall, Harry and Snape certainly aren't, so if it was based solely on emotion, a non-evil teenager who's particularly angry could still be a threat.
While it's never stated, it seems likely that Unforgivable Curses can usually only be cast by adult wizards. Except for Harry's somewhat successful Cruciatus Curse, everyone we see casting an Unforgivable Curse is 17 or older - when Harry casts them during his hunt for Horcruxes, he's 17.
In addition, that the Death Eaters don't exclusively use Unforgivable Curses in battle implies that they're difficult to cast. If they were easy spells that only required intent but not skill, then it's likely that the Death Eaters would use them more often, only using other spells in battle when they have a specific reason for that. However, use of the Unforgivable Curses is rarer than would be expected if that were true. Even Bellatrix, who is quite skilled at the Unforgivable Curses, uses other spells in battle when, if they were effortlessly cast, an Unforgivable Curse would have worked just as well.
It seems like skill does play a part - we never see a weak wizard casting an Unforgivable Curse, only wizards we know to be otherwise skilled. The Unforgivable Curse that seems to be most sensitive to intent is Crucio - it is a factor in casting the other two, but not as much.
Crucio can cause varying degrees of pain, so the more you want to cause pain, the more you do cause.
“Bellatrix screamed: the spell had knocked her off her feet, but she did not writhe and shriek with pain as Neville had – she was already back on her feet, breathless, no longer laughing. Harry dodged behind the golden fountain again. Her counter-spell hit the head of the handsome wizard, which was blown off and landed twenty feet away, gouging long scratches into the wooden floor.
‘Never used an Unforgivable Curse before, have you, boy?’ she yelled. She had abandoned her baby voice now. ‘You need to mean them, Potter! You need to really want to cause pain – to enjoy it – righteous anger won’t hurt me for long – I’ll show you how it is done, shall I? I’ll give you a lesson
Harry Potter and the Order of the Phoenix, Chapter 36 (The Only One He Ever Feared)
Harry's attempt at Crucio still worked somewhat, even though he didn't really mean it. So it seems that Crucio works better if you want to cause pain, but won't necessarily not work at all if you don't.
Avada Kedavra either works, or doesn't work. Unlike the other two Unforgivable Curses, we never see a partially effective Killing Curse. Once it's powerful enough to work, a 'more powerful' Avada Kedavra wouldn't make a difference. Dead is dead. In addition, it doesn't seem like you really have to want the person dead, or perhaps you can compensate with sufficient skill - Snape didn't really want Dumbledore to die. He knew it had to happen and it was what was asked of him, but he didn't want to do it.
“Snape raised his eyebrows and his tone was sardonic as he asked, ‘Are you intending to let him kill you?’
‘Certainly not. You must kill me.’ There was a long silence, broken only by an odd clicking noise. Fawkes the phoenix was gnawing a bit of cuttlebone.
‘Would you like me to do it now?’ asked Snape, his voice heavy with irony. ‘Or would you like a few moments to compose an epitaph?”
Harry Potter and the Deathly Hallows, Chapter 33 (The Prince's Tale)
Imperio also seems to not need any special emotion behind it to be at least somewhat effective.
Harry casts it at Gringotts. He casts it fairly successfully even the first time. His first attempt isn't the best but it does what he needed it to do. He does remember the "you need to mean them" after casting Imperio the first time.
“They’re Imperiused,’ he added, in response to Hermione and Ron’s confused queries about Travers and Bogrod, who were both now standing there looking blank. ‘I don’t think I did it strongly enough, I don’t know …’
And another memory darted through his mind, of the real Bellatrix Lestrange shrieking at him when he had first tried to use an Unforgivable Curse: ‘You need to mean them, Potter!”
Harry Potter and the Deathly Hallows, Chapter 26 (Gringotts)
However, even the very next time he casts it, it doesn't really seem like he 'really means it' or even tried to. Even if he did try, it's unlikely he could possibly mean it as much as she did.
“Good!’ said Griphook. ‘So, we need Bogrod to control the cart; I no longer have the authority. But there will not be room for the wizard.’ Harry pointed his wand at Travers.
‘Imperio!’
The wizard turned and set off along the dark track at a smart pace.”
Harry Potter and the Deathly Hallows, Chapter 26 (Gringotts)
Any time a 'good' wizard casts an Unforgivable Curse, it's clear that they wouldn't mean it nearly as much as a Dark one like Bellatrix, even if they channel all the negative emotions inside them. Yet, their Unforgivable Curses still work at least some of the time, especially for adult 'good' wizards like McGonagall and Snape.
Overall, it's likely that a wizard with the combination of skill and intent would cast the most powerful Unforgivable Curses. This is likely why Bellatrix is so good at casting them - she has both the skill and the desire.
It's unlikely that you'd need specific Dark Arts training to cast them correctly.
Harry casts two of the three Unforgivable Curses, Imperio and Crucio, during his hunt for the Horcruxes. We've seen every form of training Harry's received, and he didn't get any special education in the Dark Arts, other than being shown what they are and being told you need to mean them when you cast them.
Training in the Dark Arts may help though, but it's unclear.
Bellatrix is skilled at casting Unforgivable Curses, and she got training in the Dark Arts from the Dark Lord himself. It's unclear whether her skills at casting all of them were improved by this, though her success with the Cruciatus Curse is likely due to how much she enjoys it.
It's not related to skill, it's related to emotions and power. When Harry tortures Bellatrix in book 5, she tells him "you need to mean it" for it to work. So the wizard would have to be powerful enough, and actually want to go through with it.
Hatred rose in Harry such as he had never known before; he flung himself out from behind the fountain and bellowed, “Crucio!” Bellatrix screamed: the spell had knocked her off her feet, but she did not writhe and shriek with pain as Neville had[...]
“Never used an Unforgivable Curse before, have you, boy?” she yelled. She had abandoned her baby voice now. “You need to mean them, Potter! You need to really want to cause pain - to enjoy it - righteous anger won’t hurt me for long - I’ll show you how it is done, shall I? I’ll give you a lesson -”
We see from the story of "Half-Blood Prince" that young Malfoy was chosen to use the powerful curse on Dumbledore. We see that EVEN BEFORE graduating Hogwarts when Malfoy was 16 after only a few years training in Wizardry, he was capable to perform the curse.
Similarly, the other "unforgivable" curses such as "Crucio" which were taught in Hogwarts! was taught when they were young. We see the category of unforgivable just means that the ministry of magic will punish those who use it by sending them to Azkaban where dementors gaurd them. [In fact after Sirius escaped the security was tightened and when Harry was 14 nobody escaped until the mass break out in the following story.]
Graduation from Hogwarts doesn't necessarily prove that the magician is capable of performing difficult spells.
As far as I understand, most of wizards treat magic strictly on a need-to-know basis. Most of the spells learnt in school become completely forgotten, just like they say that an average man uses about 300 words in everyday life, though he or she does certainly know more. All I wanted to say is that we can't judge as to whether some person is capable of doing the curse after Hogwarts or not.
One of the most important parts in successful spell-casting is the emotional condition of the wizard. Remember, that magic reveals itself during childhood at the moments of the most intense emotional shakes. The students on Moody's lesson didn't possess enough emotional charge.
