What is the method in which each victim was murdered in And Then There Were None?

In And Then There Were None by Agatha Christie, eight strangers are lured to a remote island by a mysterious stranger. On their arrival, the strangers meet two other guests: a husband and wife who have also been invited to the island to work as butler and cook. The host is known only to the guests by his name U. N. Owen (Unknown). In each of their rooms is a poem by the name of "Ten Little Indians," and, in the dining room, there are ten Indian figurines on the table.
Following their dinner on the first night, the guests gather together in the drawing room. A voice suddenly resonates around the room and accuses each of the guests of murder. It tells them they have been brought to the island to face punishment. None of the guests know what to make of what they have heard until Tony Marston takes a drink from his glass and dies. He has been poisoned with cyanide.
Like the poem "The Ten Little Indians," the guests die in the same manner and in the same order.

Ten little Indian boys went out to dine;One choked his little self and then there were nine.Nine little Indian boys sat up very late;One overslept himself and then there were eight.Eight little Indian boys traveling in Devon;One said he'd stay there and then there were seven.Seven little Indian boys chopping up sticks;One chopped himself in halves and then there were six.Six little Indian boys playing with a hive;A bumblebee stung one of them and then there were five.Five little Indian boys going in for law;One got in Chancery and then there were four.Four little Indian boys going out to sea;A red herring swallowed one and then there were three.Three little Indian boys walking in the zoo;A big bear hugged one and then there were two.Two little Indian boys sitting in the sun;One got all frizzled up and then there was one.One little Indian boy left all alone;He went and hanged himself and then there were none.

Tony Marston dies of cyanide poisoning. Mrs. Rogers does not wake up. General MacArthur is killed by a blow to the back of his head. Thomas Rogers is killed with an axe. Emily Brent is killed with an injection. Judge Wargrave is supposedly killed with a gunshot to the head. Blore is crushed by a clock. Dr. Armstrong is drowned in the sea. Phillip Lombard is shot with his own gun. Vera Claythorne hangs herself.