How can I authenticate users in a java android application using sharepoint 2013 and secondly how to authenticate users using active directory directly. I have to implement
Azure provides an API for authentication for Microsoft Sharepoint. You can login using that else you can open webview for login of sharepoint. Then after login you can store cookies and you can use it as token in each webservice call.
For more detail about azure you can see this link .
Azure API For Microsoft sharepoint
sample code for azure authentication
If you want to login with webview then you can see this link below it helps you. Login with Webview