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“Your most unhappy customers are your greatest source of learning.” – Bill Gates
Customer feedback is an important way to measure product success, and to determine new directions for your product or company.  However, aside from a few “squeaky wheels,” most customers will not proactively offer their thoughts and feedback without being prompted.  There are essentially two  ways to achieve this, through active feedback and through passive feedback.
Active
Active feedback involves talking directly to customers.  The specific method you choose depends on your product or service.  You can offer live chat on your website.  Having an option for instant dialogue increases the likelihood that customers or potential clients will ask questions they may have about your product or service, instead of putting the questions off until later and then forgetting about them.  Similarly, you can also prompt users and prospects to take surveys.  Wufoo, Intercom,  and UserMood  are two easy ways to do this.  Wufoo uses a web-based survey platform that directs your target audience to complete a survey on their site, where the results are stored for your analysis.  UserMood and Intercom accomplishes many of the same functions, but provides the service embedded directly in your app.  You may consider offering a contest in conjunction with your survey.  Featuring a prize or raffle will motivate users to complete it, and thus increase your survey response rate.  This works well if you have a smaller target audience and need feedback from a higher percentage of them to get a sense of your customer base.  Finally, you can contact customers directly via email or cold calls to ask them a set of pre-determined questions.
Passive
Passive feedback relies less on customer-driven answers and more on metrics.  Many of these options are less time-consuming and offer a “set-it-and-forget-it” approach to collecting data.  The first item you want to measure is return customers.  How many of your customers are pleased enough with your product to purchase it again?  What is your average subscription length (What is your customer lifetime value?)?  Set up your business in such a way that you can track this information easily as time goes on.  Similarly, how much of your business comes through referrals?  Whether or not you choose to offer a discount or credit for referrals, make it easy for customers to share your product with their friends, through social media buttons or email reminders.  Provide a separate referral form or link, so that you can track referrals independently.  A third passive method is finding out what customers have to say about your product.  Set up Google Alerts or Twitter searches that ping you when your product or service is mentioned.  Be proactive in providing channels for customers to talk about your products through social media links on your product website.  Finally, be cognizant of online reviews, and observe what people are saying on Google, Yelp!, CitySearch, and other sites.
The best method of customer feedback will depend on you and your product.  If you need a quick and dirty method to gauge overall satisfaction, look to passive feedback.  If you want to drill down a bit further, or try to identify potential problems, opt for active feedback.  Either way gives you the opportunity to learn more about your customers and become more efficient at meeting their needs.