Best way to create a User Account database?

Basically I'm hoping someone can point me in the right direction with the most secure/safest way to create and store user accounts.

Essentially what I want to do is have the user enter their login credentials through my Android app and then simply load up their info on the app. So I need to verify the credentials and then pull their information afterwards.

Many of the login systems I've seen seem similar so I'm guessing there's an API/Library out there somewhere, but I don't really know where to go about finding it.

Also in terms of actually storing the information, I'm guessing I'll need to store it on a database (SQL?); but how do I ensure it's stored there securely?

EDIT: I should probably mention that I'll be doing all this in Java.

Thanks in advanced to anyone who can shed some light on this for me!