The state of mind
Next to Anthony's answer I think it is inevitable to really mean it. For that I would quote:
“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 Phoenix, ch. 36, The Only One He Ever Feared
And Harry after performing Crucio for real:
As Amycus spun around, Harry shouted, “Crucio!” The Death Eater was
lifted off his feet. He writhed through the air like a drowning man,
thrashing and howling in pain, and then, with a crunch and a
shattering of glass, he smashed into the front of a bookcase and
crumpled, insensible, to the floor. “I see what Bellatrix meant,” said
Harry, the blood thundering through his brain, “you need to really
mean it.”
Harry Potter and the Deathly Hallows, ch. 30, The Sacking of Severus Snape
I would say it is a bit similar to what you have to do to conjure the Patronus. For the Patronus, you need to concentrate on very happy memory, something hopefull. When you perform Unforgivable Curses you need to do it without hesitation, so your mind is fully concentrating, as we can see from the first quote - pure anger is obviously not enough.
Similar situation with Imperio
Although this is not precisely what OP wanted, I think it is related:
Next to the things I said above, I was always suprised how easily it seemed for Harry to cast Imperio:
“Act now, act now,” whispered Griphook in Harry’s ear, “the Imperius
Curse!” Harry raised the hawthorn wand beneath the cloak, pointed it
at the old goblin, and whispered, for the first time in his life,
“Imperio!”
And after a few moments again:
Harry acted without thinking: Pointing his wand at Travers, he
muttered, “Imperio!” once more.
It is true, that this was really tight situation and he had to act quickly. But I was a bit impressed, that it worked the first time. But it is true, that if we would like to somehow sort the Unforgivable Curses by the complexity and difficulty, the Imperio would probably ended up at the bottom of the list.
Other mentions of Avada Kedavra
I also looked up the situations where Avada Kedavra is casted. But there is not very much we can tell. The books characters often only says the incantation:
“I have nothing more to say to you, Potter,” he said quietly. “You
have irked me too often, for too long. AVADA KEDAVRA!”
Harry Potter and the Order of Phoenix, ch. 36, The Only One He Ever Feared
Snape raised his wand and pointed it directly at Dumbledore. “Avada
Kedavra!” A jet of green light shot from the end of Snape’s wand and
hit Dumbledore squarely in the chest.
Harry Potter and the Half Blood Prince, ch. 27, The Lightning-Struck Tower
“It’s that Mudblood! Avada Kedavra!”
Crabbe wheeled around and screamed, “Avada Kedavra!” again.
Harry Potter and the Deathly Hallows, ch. 31, The Battle of Hogwarts
I think the only one, that mentions something more is in this case:
Voldemort was ready. As Harry shouted, “Expelliarmus!” Voldemort
cried, “Avada Kedavra!”
...
Harry, following the beam with his astonished gaze, saw
that Voldemort’s long white fingers too were gripping a wand that was
shaking and vibrating.
...
The closer that bead moved, the harder Harry’s wand vibrated; he was
sure his wand would not survive contact with it; it felt as though it
was about to shatter under his fingers — He concentrated every last
particle of his mind upon forcing the bead back toward Voldemort, his
ears full of phoenix song, his eyes furious, fixed... and slowly,
very slowly, the beads quivered to a halt, and then, just as slowly,
they began to move the other way... and it was Voldemort’s wand
that was vibrating extra-hard now... Voldemort who looked
astonished, and almost fearful....
Harry Potter and the Goblet of Fire, ch. 34, Priori Incantatem
Although the vibrating and other stuff might be happening because of the Priori Incantatem phenomen, it might hint a bit. Also I've marked the the part with Harry, although he casted Expelliarmus it illustrates the principles, that can happened behind some kind of magical fight. It is both physical and mental challenge. But, yes this goes still more away from the topic.