They key question you need to answer is this: What is your goal? Why are you doing such analysis in the first place? Do you want to identify where your users are coming from and what they are looking at, so you can tailor your content to your audience… or are you wanting to find out specific “soft” characteristics such as age or education (which will not show up in web analytics)? Are you looking to capture demographic information to support ad sales and focus content?
To underline my point, what you are looking for informs the approach and the data you gather and analyze. And when it comes to analysis, the best way is to take your data and throw it into a tool like excel and look for trends and organic groupings. You can use built-in tools like sort, filter and pivot table to get a better grasp of the data.