iPhone 5s not registering steps data in iOS 8 Health app
See Edit note at bottom.  My answer does need work, but I don't know the correct answer yet.

You need additional accessories to collect that data. 

From the IOS8 for iPhone manual Page 122:


  Data sources: Enter your own data, Collect data from a device, Collect data from an app.


Also on Apple's "Health" marketing page note it says:


  The Health app in iOS 8 lets you see the data that your health and fitness apps collect in one place. You can also store your important health data in Medical ID for easy retrieval in an emergency.


Nowhere in any of the documentation does it indicate that Apple has figured out a way to collect this data with the phones sensors regardless of where the user is keeping/carrying the phone (i.e. shirt pocket, pants pocket, in an arm band carrier...etc).  

Apple also sells the accessories in the apple store.

EDIT to add:  Now I'm confused too!! today My iPhone 6 has data collected, and I don't know how from the research I've done for this answer. The interface seems incredibly buggy, I am seeing both NO DATA and graphs populated with data and I can't see apparent methods to make either happen intentionally.  Drilling down to the "All Data" display and waiting a long time does seem to return data points that the phone has collected.   

Additional Info Edit: NO DATA seems to appear while data is being sorted, that's my feeling anyway, I can't seem to figure out what makes sorting short or long however.

I've googled and searched apple additionally and can find no apparent documentation other than what I've already linked and quoted.