Now that you've brought your survey to your audience's attention, you will still have to motivate them to fill it out. The simplest and most common solution is to offer some incentive to complete the survey. If you run a commercial website, an obvious incentive is a coupon. I know that some of you may cringe at the thought of cutting into your margins just to get someone to answer a few questions for you, but you have to keep the big picture in mind.
If you take the time to craft your survey carefully, you can acquire information on your website's audience that you would otherwise never get. This information will not be from broad industry data, it will be from your current audience. Could you sell a product better if you knew more about who you're selling it to?
But maybe you aren't selling a product. Maybe you can't offer a coupon, what do you do then?
There are many community websites that don't sell products themselves and generate revenue from advertising. In this instance coupons would have to come out of your own pocket. If you've got pressing questions in your survey that you need answered immediately, then you may not mind investing those funds. But if this does pose a problem for you, you can seek out alternatives. You could get in touch with your advertisers and see if you can work out some type of agreement, perhaps a discount on additional ad space in return for a number of coupons. If this doesn't sounds like something that would work for you, then you may want to consider community incentives.