I was looking at the Area 51 stats, and I noticed something interesting. With 2 exceptions, myself and Amber, every one of the users on the top page thus far has exclusively asked or answered questions. The truth is, we need both. People who are willing to ask good questions that many amateurs have, even if they know the answer already. Also, people answering said questions. It's even okay to answer your own question, there's even a badge for it. Bottom line is, we really should encourage people to both ask and answer questions!
First: on any StackExchange site you're going to have a lot of people who do only one or the other (e.g. on StackOverflow I have 3000+ answers and exactly 2 questions). That's simply a fact of life. As long as you have a good number of both of those types of people, you're fine; you'll get plenty of questions and plenty of answers.
That said, the best way to encourage each type of action is through votes. Vote on questions. Vote on answers. It's kind of shallow, but there are people who do things on these kind of sites for the rep. If they see asking questions as a good way to make rep, they'll ask questions (and if good questions get more votes, they'll try to ask good questions).
The same goes for answers. Vote up good answers. Try not to dogpile on mediocre ones. If you asked a question, make sure to eventually accept an answer (assuming any of them are good). People will react to that.
We don't need to get people to do anything.
People who ask good questions are very welcome here, whether they answer any questions or not.
People who create good answers are very welcome here, whether they ask any questions or not.
People should be encouraged for making a positive contribution and Amber's perfectly explains how to do that.