Before you ask
When you ask your question, display the fact that you have done these things first; this will help establish that you're not being a lazy sponge and wasting people's time. Better yet, display what you have learned from doing these things. We like answering questions for people who have demonstrated they can learn from the answers.
Use tactics like doing a Google search on the text of whatever error message you get (searching Google groups as well as Web pages). This might well take you straight to fix documentation or a mailing list thread answering your question. Even if it doesn't, saying “I googled on the following phrase but didn't get anything that looked promising” is a good thing to do in e-mail or news postings requesting help, if only because it records what searches won't help. It will also help to direct other people with similar problems to your thread by linking the search terms to what will hopefully be your problem and resolution thread.
Take your time. Do not expect to be able to solve a complicated problem with a few seconds of Googling. Read and understand the FAQs, sit back, relax and give the problem some thought before approaching experts. Trust us, they will be able to tell from your questions how much reading and thinking you did, and will be more willing to help if you come prepared. Don't instantly fire your whole arsenal of questions just because your first search turned up no answers (or too many).
Beware of asking the wrong question. If you ask one that is based on faulty assumptions, J. Random Hacker is quite likely to reply with a uselessly literal answer while thinking “Stupid question...”, and hoping the experience of getting what you asked for rather than what you needed will teach you a lesson.
Never assume you are entitled to an answer. You are not; you aren't, after all, paying for the service. You will earn an answer, if you earn it, by asking a substantial, interesting, and thought-provoking question — one that implicitly contributes to the experience of the community rather than merely passively demanding knowledge from others.
On the other hand, making it clear that you are able and willing to help in the process of developing the solution is a very good start. “Would someone provide a pointer?”, “What is my example missing?”, and “What site should I have checked?” are more likely to get answered than “Please post the exact procedure I should use.” because you're making it clear that you're truly willing to complete the process if someone can just point you in the right direction.