Hi @jason-naparstek and welcome!  No this topic hasn’t been covered that extensively and it’s a great topic!

Since I’m not an App developer, I don’t have a wide experience but I do see ads for Apps.  I don’t know how they perform.  You can see who is advertising to your demographic by going to http://www.facebook.com/ads/adboard.  It doesn’t show all the ads, just the ones that match your profile target.  
I have talked to app developers and I know a big part of  the “viral” nature of Apps can be the permissions you request and how you post to the timeline when people are using your app.  Things you can do to get more attention for your app is to do traditional marketing techniques like getting blogs to cover your app, doing guest posting for sites that are in your target market, advertising is good, and building a following on social media.  

But I would love to hear from anyone who has developed an app on how they get the word out!

Also, you can search topics in the clubs.  One way is to use the search bar in the upper right and look for the topics that say forums versus articles.  You can also look at tags here and click on tags on a topic to see all the topics that have that tag.  The search is a bit challenging so it doesn’t always find everything.

@jason-naparstek

Hi Jason,

I didn’t run the Ads for the app yet but I’m running small app with few thousands of active users monthly.

I would recommend you to utilize the power of new Open Graph actions and objects. It can bring you a lot of users for free and you can also transform actions of your users into Ads and promote them – and they are closely related to the viewers, like “Mary cooked the Baked rolls in CookSomething“
You can find more about the Open Graph and how it works here:

https://developers.facebook.com/docs/opengraph/

And as you were asking for insights, the key metric is the number of Monthly Active users, then you can check for conversion rate of your Permissions dialog (as Andrea mentioned, you can lose a lot of users there). 

You can see if your users are coming back in section “Users -> Retention”. It is also good to watch the negative feedback that your app receives from users.

Are you interested in something more specific?

Lada