Tip 1: Here is the Facebook Insights Guide. Read it.
Tip 2: Track the People Talking About metric for your brand and your competitors to see how engagement levels fluctuate.
One of the most obvious changes is displaying the number of people who are 'talking about' your page. Its like Klout for brand Pages!
Facebook describes this metric as "How many people are actually talking about your brand or company to their Facebook friends."
It is broken down to each individual post and includes everyone who:
• Liked your Page
• Liked, commented on, or shared your Page post
• Answered a Question you’ve asked
• Responded to your event
• Mentioned your Page
• Tagged your Page in a photo
• Checked in or recommended your Place
Note that this does not include Wall Posts by anyone other than the brand. Data from 19th July 2011 is available on the new Page Insights.
Tip 3: Check if your ads are even working using the Total Reach analysis
The Total Reach metric shows the number of unique people who have seen your post, broken down by Organic, Paid and Viral reach for your post. This will help you track whether your paid advertising is working. For example, if you are getting a high paid reach on a post (via Sponsored Page Post or Sponsored Stories) but your other engagement metrics (below) are not improving, then your ads are probably not targeting the right audience, or are not interesting or relevant enough to that audience..... and so they just don't click on the post. Its unfortunate that the scale on the graph can make your viral statistics seem very low - make sure you hover over the purple viral bar to see how many times a friend of one of your Fans saw your post as a result of the Fan liking, commenting or sharing your post.
The metric Engaged Users is important and tells you the unique number of people have clicked anywhere on your post - whether it was playing a video, viewing the full size of a photo, clicking a link, sharing your post, commenting or liking it, clicking on people's names or the timestamp.
Under the Fans tab of the Page Insights you can see further analysis of who your Fans are including age, gender and country. This graph will show you where your Page Likes are coming from (eg via the Newsfeed, on a mobile phone, on your website or elsewhere)
You might have one age demographic which dominates your Page Fans, however they may not actually be the age or gender demographic who are engaging with your posts. Find out who is most engaged on your page on the Talking About tab of Page Insights - you might be surprised.
Lastly, here is a quick snapshot of some of the Talking About metrics for a selection of Facebook Pages you might be familiar with - makes interesting reading. Also check these stats again in a few weeks to see how these metrics change over time.