What can you infer the story will be about based on the title?
This is an interesting question. The story turns out to be largely about a poisonous snake. But the author could not dare to mention the word "snake," especially in the beginning when Helen Stoner is telling her long back story to Holmes and Watson. Any mention of the word "snake" would immediately make the reader strongly suspect that Dr. Grimesby Roylott had used a poisonous snake to kill Julia Stoner and was using the same snake to try to kill his other stepdaughter Helen. So in Helen's back story during her consultation with Holmes, she cannot say that her sister saw a snake. Here is what she says her sister told her:
‘Oh, my God! Helen! It was the band! The speckled band!’ There was something else which she would fain have said, and she stabbed with her finger into the air in the direction of the doctor's room, but a fresh convulsion seized her and choked her words.
Assuming that Julia saw the snake and recognized it as a snake, the only explanation we can offer for her calling it a "speckled band" rather than a snake would be that she was delirious. She might have been trying to say, "It was a snake that looked like a speckled band." She was pointing at the doctor's room to indicate that she accused her stepfather of sending it through the ventilator to kill her.
Once the author had thought of the term "speckled band" he must have decided to use it in his title in order to tell what the story was about without actually telling too much. Holmes thinks the speckled band must refer to a band of gypsies who camp on the grounds at Stoke Moran. Even when Holmes is beating the snake in order to drive it back up the bell-rope, he does not say the word "snake." And when they go into Dr. Roylott's room where they find him dead, Watson does not use the word "snake" either. Here is his description of the sight both men see:
Round his brow he had a peculiar yellow band, with brownish speckles, which seemed to be bound tightly round his head. As we entered he made neither sound nor motion.
“The band! the speckled band!” whispered Holmes.
It isn't until the snake moves that Watson sees what it really is:
I took a step forward. In an instant his strange headgear began to move, and there reared itself from among his hair the squat diamond-shaped head and puffed neck of a loathsome serpent.
I don't believe a person reading the story for the first time could infer much of anything from the title. That must have been Arthur Conan Doyle's intention. The title piques the reader's interest without telling him too much. The whole story is built around the idea of a man using a snake to kill a woman who appears to be perfectly safe in a room with the door locked and the shutters tightly bolted. So the reader, like Holmes himself, can only guess at the meaning of the words "speckled band," and like Holmes the reader may suspect that the band of gypsies must have been involved in Julia Stoner's death. That doesn't leave Dr. Roylott in the clear. He could have paid the gypsies to kill his stepdaughter. These false clues are intended to divert the reader from guessing the actual truth. The word "band" is ambiguous, and especially so when there is a band of gypsies involved.
Arthur Conan Doyle handles his premise very well. He was an excellent writer. There is something he doesn't mention in his story because of Victorian prudery; but it must occur to most readers after having finished reading about the solution to the mystery. That snake must have been on Julia's bed at least four times, including the time it finally bit her. We know this because she tells her sister she has heard the low whistle three times before the night of her death. Holmes states early in the story, both to Helen and to Dr. Roylott, that the weather is very cold. The snake is an Indian swamp adder. It is from a hot, humid country. When it crawled down the bell-rope onto Julia's bed, it would not have tried to escape from the room and from the house because of the cold. Instead it would seek warmth. And on four nights in a row it probably crawled right under the bedcovers and curled up beside the sleeping girl's warm body. It would not have bitten her unless she did something threatening. Helen tells Holmes that when Julia died:
In her right hand was found the charred stump of a match, and in her left a match-box.”
Evidently when Julia heard the low whistle she turned over in bed to reach for the box of matches and rolled right on top of the snake. The swamp adder would have bitten her through her nightgown, so the bite-mark would not have been visible. At the autopsy the bite-mark could have been overlooked because no one would have expected to find any wound down around her abdomen. Julia probably did not have matches available on the first three nights she heard the whistle. But since she was getting very concerned, as she told her sister, she must have made sure to have the box of matches and a candle right beside her bed on the night she met her death.