I think this question is a little vague, you need to clarify what exactly you are trying to do. I'd also question whether EE makes a good backend for any sort of mobile app, you are probably better off writing your own backend app directly in PHP, or looking at something like Parse, however, I digress.
The principles are simple enough. This has already been done by Mountee, for example. To log in to EE from a native app, there are three steps:
- Generate an XID (just request the login page, and parse the response to get an XID value). If you create your own PHP login script you can avoid this requirement.
- Submit the login form
- Record the session cookie in your app and use it for future requests
As far as actually creating new members in the database - it is best to use the built in EE functions as much as possible for this. The EE member API is a bit of a minefield, and wasn't written with re-use in mind. However, with some tricks it is possible to call the functions and avoid any issues which may arise from changes to the database schema in future.
Your best starting point is probably to take a look at the open source Freemember plugin, which allows you to create front-end member registration & login forms. You could also use its library which abstracts the process of registering new members.