We've developed the first version of our website and going to lunch it and introduce it to a crowd. How do we know which part of our work has weakness and how we should correct it?
You can of course use analytics that will give you statistics, but will not answer "Why?". Gathering Customer Feedback is crucial and You have to be preprared for low response rates. For better understanding of Customers' interactions with Your site You can use tracking/heatmap solutions (i.e. Crazy Egg or Hotjar). But most important is to define goals and identify steps that lead to them - what do You expect Customer will do or act like? What needs to be done to acheive it? Then start monitor those steps, gather feedback, mae changes and see if this works looking at stats.