Dave McClure's Startup Metrics for Pirates
(AARR!) is the seminal work on measuring the success of your cat photo / specially coffee / sharing economy app. The beauty of AARR! (besides pirates) is it's simplicity: you can quickly apply it your business without taking an economics class.
I'll walk through each of the metrics, which metrics you should focus on for each stage of your startup, and some examples. We've used these metrics at Scout at each stage of our company - from boostrapped launch to solid growth. I'll also share the tools we've used to collecting this data.