If I had only one hour to solve a problem, I would spend up to two-thirds of that hour in attempting to define what the problem is. — Anonymous Yale professor (often wrongly attributed to Einstein)

Asking questions is a core skill for professionals. Asking questions to know, to understand, to probe, to test. Anyone can feel exposed asking questions, because they feel like they should know or understand already. If novices and 'experts' alike have trouble asking questions, if your community or organization does not foster a culture of asking, then there's a problem.

What is a good question?

There are naive questions, tedious questions, ill-phrased questions, questions put after inadequate self-criticism. But every question is a cry to understand the world. There is no such thing as a dumb question. — Carl Sagan

Asking good questions is the best way to avoid the problem of feeling silly or — worse — being thought silly. Here are some tips from my experience in Q&A forums at work and on the Internet:

Do some research. Go beyond a quick Google search — try Google Scholar, ask one or two colleagues for help, look in the index of a couple of books. If you have time, stew on it for a day or two. Do enough to make sure the answer isn't widely known or trivial to find. Once you've decided to ask a network...
Ask your question in the right forum. You will save yourself a lot of time by going taking the trouble to find the right place — the place where the people most likely to be able to help you are. Avoid the shotgun approach: it's not considered good form to cross-post in multiple related forums.
Make the subject or headline a direct question, with some relevant detail. This is how most people will see your question and decide whether to even read the rest of it. So "Help please" or "Interpretation question" are hopeless. Much better is something like "How do I choose seismic attribute parameters?" or "What does 'replacement velocity' mean?".
Provide some detail, and ideally an image. A bit of background helps. If you have a software or programming problem, just enough information needed to reproduce the problem is critical. Tell people what you've read and where your assumptions are coming from. Tell people what you think is going on.
Manage the question. Make sure early comments or answers seem to get your drift. Edit your question or respond to comments to help people help you. Follow up with new questions if you need clarification, but make a whole new thread if you're moving into new territory. When you have your answer, thank those who helped you and make it clear if and how your problem was solved. If you solved your own problem, post your own answer. Let the community know what happened in the end.

If you really want to cultivate your skills of inquiry, here is some more writing on the subject...

How do I ask a good question? — advice from the world's biggest Q&A site
How to ask questions the smart way — by open-source hacker Eric Raymond
Ten tips for asking good questions — from For Dummies
How to be amazingly good at asking questions — by Mike Martel
How to cultivate the art of asking good questions — Warren Berger, A More Beautiful Question

Supply and demand

Knowledge sharing networks like Stack Exchange, or whatever you use at work, often focus too much on answers. Capturing lessons learned, for example. But you can't just push knowledge at people — the supply and demand equation has two sides — there has to be a pull too. The pull comes from questions, and an organization or community that pulls, learns.

Do you ask questions on knowledge networks? Do you have any advice for the curious?