There is a game you can play that helps you get better at asking questions. The goal in an information gathering session is to gather information and you gather information by asking questions so the idea is to say nothing that is not a question after the introductions are over. It can be done.
Here is the game. The original name of the game is Rosencrantz and Guldernstern. The game was introduced in the Tom Stoppard play “Rosencrantz and Guldernstern are Dead”. I’ve also heard it referred to as “tennis” or “verbal tennis”.
Rules are simple. Two players. One person starts by asking the other a question. The other must respond to the question with another question based on what was asked. Then the first responds with a question and so on. They have a conversation all in questions. If a player responds with anything but a question or takes too long to answer, the player is “buzzed out” and a new player takes his or her place. The winner is the one who stays longest without getting replaced. Good party game.
To win the game ask closed ended questions. People tend to answer the closed ended questions without thinking.
However, a better result is a more cooperative everyone wins. Consider the tennis match where the object is to keep the ball going across the net for the longest time rather than beat the opponent.
In this case the way to keep going is to focus on the last words or phrase the person makes and form a question around those words. You can do this in a meeting or interview as well, and it is easier since the responder is not asking you questions (or shouldn’t be asking). Ask the question even when you know the answer (as long as the question is not overly obvious). Asking the question has several positive results
1. you get information
2. The person whose last words you reference is flattered because you are clearly listening to what they are saying and appear to have an interest in their thoughts and answers – they will give you more information willingly
3. Others listening will also feel more encouraged to join in, especially if they know the answers. (remember the natural tendency of us all to mentally try to answer a question when asked of someone else – hence the continuing popularity of Jeopardy.)
4. The interchange and continuing answers get everyone involved and feeling good about their involvement
Try it.

Sam and Tracey,
My favorite way to ask questions while the session is in progress is to just be silent for a moment. Often from the silence comes something – whether from me or the stakeholder. Another “trick” is to ask “is there anything I should be asking or we should be talking about?” Or, just to pause for a moment, look over my notes, and see where the gaps are, then pose a question to fill in the gap. You could look at it as an art, but I think patience with oneself as well as the confidence to allow for some awkward-feeling silence can go a long way.

Sam, yes I think you’re right, it’s a practiced art, so I’m discovering. I think a degree of patience is required also. I think a degree of understanding their situation is a must (Steve, I think you’re aluding to this) and ensuring you are adding value. I will continue to learn!
Thank you all.

Thank you Sam, I’ll add Survey Monkey into my’ Rabbit’s Hat’!