We know for a fact that Basilisk venom is one of the few substances strong enough to destroy a Horcrux. Not only does it destroy the one inside Tom Riddle's diary, but Ron and Hermione also use one of the fangs to destroy Helga Hufflepuff's cup.
Basilisk venom isn't the only substance that can destroy Horcruxes. We know for sure that Fiendfyre can get the job done, and based on Hermione's explanation, there are probably at least two or three other substances that could do it, too.
The diary was the first of Lord Voldemort's Horcruxes to be destroyed, by Harry Potter in the Chamber of Secrets, who stabbed it with the fang of the very Basilisk that was used to commit murder in the first place.
Basilisk venom is extremely powerful, and can kill a person within a little more than a minute at best, making the person drowsy and blurry-visioned before they die. The strength of the venom is one of the few substances known to be capable of destroying Horcruxes, causing them fatal damage that cannot be repaired.
Why didn't Dumbledore think of using a basilisk fang to destroy the horcruxes? He was considered a genius, he knew there was a dead basilisk in the chamber of secrets at Hogwarts and that Harry destroyed Tom Riddle's diary with its fang but instead of doing it the simple way, he kept thinking of other ways.
Horcruxes can only be destroyed in specific circumstances that allow it's complete and utter destruction. In the movies, the Horcruxes are destroyed in these ways: The killing curse — “Avada Kedavra.” Fiendfyre — a curse that creates powerful and magical flames.
Voldemort intentionally made six Horcruxes, but when he used Avada Kedavra on Harry, he unintentionally created a seventh Horcrux. Instead of dying, Lily's love for Harry created a counter 'curse' known as Sacrificial Protection and saved Harry.
Hermione Granger and Ron Weasley destroy the Hufflepuff's cup Horcrux inside the Chamber of Secrets—Hermione giving it the fatal blow with a basilisk fang.
Dumbledore would eat the Basilisk for breakfast. Never mind you not looking at it, he can use charms to extend his senses without looking and he is very most certainly powerful enough to kill it any time of the day if he knows where it is.
He couldn't
Creating a Horcrux requires a number of foul rituals. These rituals, crucially, may take time. Voldemort might have needed to spend days or weeks in the chamber in order to turn the Basilisk into a Horcrux.
Harry is never immune to the basilisk's look, I repeat look. The basilisk was blinded by Dumbledore's phoenix (Fawkes). So technically the basilisk could not see Harry or turn him into stone.
Though Harry encountered many opportunities that deemed Avada Kedavra necessary, it remains as one of the Unforgivable Curses Harry Potter never cast. For one, he viewed the spell as an immoral practice commonly used by users of the Dark Arts.
The Avada Kedavra – the killing curse from the Harry Potter Wizarding World is unforgivable, cannot be blocked, and is colored green.
Kreacher returned to Grimmauld Place, unable ever to tell Mistress Black what had happened to her son, and unable to destroy the locket as ordered because of the powerful enchantments protecting it.
So when Ron said three, it wasn't a mistake. He meant there were three more horcruxes to destroy before being able to destroy the fourth and final piece which was in fact Voldemort himself.
Quirrell is, in effect, turned into a temporary Horcrux by Voldemort. He is greatly depleted by the physical strain of fighting the far stronger, evil soul inside him.
The Locket
Of all of Lord Voldemort's Horcruxes, Salazar Slytherin's old locket is the most difficult to obtain and destroy. In the Half Blood Prince, Harry Potter and Albus Dumbledore travel to an old cave where the Dark Lord would torture victims during his time as a teenager.
Draco Malfoy's mother Narcissa was cold, cunning and devoted to the Dark Lord. But she was also a mother, which meant she was willing to risk everything to make sure her son was safe. When Harry survived Voldemort's Killing Curse for the second time, Narcissa pretended he was dead so she could get to Draco.
Her sacrifice gave Harry the power of love, a protection spell sealed with the blood spilled by her death.
This theory suggests that each time he created a new Horcrux, that specific Horcrux diminished a part of his soul. Thus, his nose began to sink in, eventually disappearing altogether. Due to his tampering with dark magic, his human appearance evolved into a more snake-like state.
Alohomora, which is a spell that unlocks objects (and it's also Hermine Granger's signature spell).
But when Ron and Hermione are about to die by Nagini, Ron casts the killing curse as a last resort and it simply rebounds off Nagini as it was nothing.