Well, lots of ways.  Browser Metrics. Crawls of the web. I don't really care for the number of views on an article or video, or downloads of a sample etc they are vanity metrics.  Use is the most important thing for us and it is what I encourage my team to focus on.

One example is Pete LePage's theme-color post it had a decent number of views, talked about on many blogs but the stat we were looking for were the number of sites that used it and if developers and users liked it.  We had a crawl of the web and found after two months over 20k sites were using (or there abouts) and that was above what we felt was good.

We work side-by-side with eng (because we are eng) and we agree on the goals of the product and we then work out the plan to how we get the adoption it needs.  

The same applies for the manifest, and service worker.  We are not helping to change the web if people don't use the API's we as an industry create, the tools the industry provides and the guidance we design.

One thing that I like, is that we help direct the product and shape the api's and features because as Advocate we have a good sense of what developers want and how they would use it.  If we don't think it fits well, we help steer and shape the product - sometimes it works well, others we have a miss, but the important thing is that as a DA you provide that channel and insight on behalf of the developer community.  I look at Jake Archibald as an example of this, he has worked directly on the Service Worker (and many other specs) and likewise Ilya Grigorik because at this early stage we can help shape the API's and tools that every devloper will use.... 6 months ago no usage metric made sense (other than feedback from X early adopters), now it is much more concentrated on implementation based goals.... At least for the team I run.

I could talk about this for a long long time, but Gauntface covers it well too in the comments.  I am putting a lot of thought about trying to shape industries based on customized guidance.  I recently presented at a Finance event, I don't measure that or the number of people who turned up, what I am setting up is do our other teams have the tools to make those sites and partners better and do they change and perform better themselves.