How can I get them asking the right questions without my leading them around by the nose?

If players chase a trail that you haven't thought out, follow the advice laid out in the other answers here, which basically say: make it the right trail. That's good advice. I'll try to add something else, which is: "How do I not end up having to do this?"

#Define "wrong question"#

Have you ever seen I, Robot? In my opinion, it has a nicely done little part where a hologram of a murdered person can answer only a specific set of questions.

Dr. Lanning's Hologram: Everything that follows, is a result of what you see here.
Detective Del Spooner: What do I see here?
Dr. Lanning's Hologram: I'm sorry, my responses are limited. You must ask the right questions.
Detective Del Spooner: Is there a problem with the Three Laws?
Dr. Lanning's Hologram: The Three Laws are perfect.
Detective Del Spooner: Then why did you build a robot that could function without them?
Dr. Lanning's Hologram: The Three Laws will lead to only one logical outcome.
Detective Del Spooner: What outcome?
Dr. Lanning's Hologram: Revolution.
Detective Del Spooner: Whose revolution?
Dr. Lanning's Hologram: [Smiles] That, detective, is the right question.

It works in the film because Spooner's a smart guy and the plot requires that eventually he figures out what the right questions are. But if you were Spooner, and you were not actually a professional detective, and you were not actually in a physical, real world where there may be more than one way to skin a cat, you'll be lucky to figure this one out.

And, man, you would hate this hologram.

#The Rule of Three Clues#

Justin Alexander has written a brilliant piece on this. I suggest every GM to read it in full, but I'll try to summarise:

Clues that appear really, really obvious to you are not obvious to your players. You have Creator Knowledge, which means that you can tell the usual from the unusual, the trivial detail from the useful clue, the Jane Random Doe from the sneaky informant. Your players don't have that: they can't tell likely from unlikely or important from trivial. They're going to miss important clues, so make sure to leave lots of important clues.

The rule of thumb is to leave three separate clues using separate mechanisms that lead to the same result. You want to find out where your southern vampire lives? Leave three clues, and make sure you don't need the other two. This means you can leave your players more initiative without having to say: "I don't have a way to make this work."

Can't find a way to leave three decent clues? Maybe the information you're trying to convey is too specific, and needs to be aggressively divulged rather than teased open. (Think of it: if you can't figure it out, how will your players ever?)

Not only will this be helpful for your players, who can suddenly carve their own path and still follow the plot you prepared, but you'll end up creating a more involved, consistent world, which will make improvising easier for you and more rewarding for you players.

How can I get them asking the right questions without my leading them around by the nose?

If players chase a trail that you haven't thought out, follow the advice laid out in the other answers here, which basically say: make it the right trail. That's good advice. I'll try to add something else, which is: "How do I not end up having to do this?"

Define "wrong question"

Have you ever seen I, Robot? In my opinion, it has a nicely done little part where a hologram of a murdered person can answer only a specific set of questions.

Dr. Lanning's Hologram: Everything that follows, is a result of what you see here.
Detective Del Spooner: What do I see here?
Dr. Lanning's Hologram: I'm sorry, my responses are limited. You must ask the right questions.
Detective Del Spooner: Is there a problem with the Three Laws?
Dr. Lanning's Hologram: The Three Laws are perfect.
Detective Del Spooner: Then why did you build a robot that could function without them?
Dr. Lanning's Hologram: The Three Laws will lead to only one logical outcome.
Detective Del Spooner: What outcome?
Dr. Lanning's Hologram: Revolution.
Detective Del Spooner: Whose revolution?
Dr. Lanning's Hologram: [Smiles] That, detective, is the right question.

It works in the film because Spooner's a smart guy and the plot requires that eventually he figures out what the right questions are. But if you were Spooner, and you were not actually a professional detective, and you were not actually in a physical, real world where there may be more than one way to skin a cat, you'll be lucky to figure this one out.

And, man, you would hate this hologram.

The Rule of Three Clues

Justin Alexander has written a brilliant piece on this. I suggest every GM to read it in full, but I'll try to summarise:

Clues that appear really, really obvious to you are not obvious to your players. You have Creator Knowledge, which means that you can tell the usual from the unusual, the trivial detail from the useful clue, the Jane Random Doe from the sneaky informant. Your players don't have that: they can't tell likely from unlikely or important from trivial. They're going to miss important clues, so make sure to leave lots of important clues.

The rule of thumb is to leave three separate clues using separate mechanisms that lead to the same result. You want to find out where your southern vampire lives? Leave three clues, and make sure you don't need the other two. This means you can leave your players more initiative without having to say: "I don't have a way to make this work."

Can't find a way to leave three decent clues? Maybe the information you're trying to convey is too specific, and needs to be aggressively divulged rather than teased open. (Think of it: if you can't figure it out, how will your players ever?)

Not only will this be helpful for your players, who can suddenly carve their own path and still follow the plot you prepared, but you'll end up creating a more involved, consistent world, which will make improvising easier for you and more rewarding for you players.