For User Authentication you can use combination of app and server side technology.
1. create registration module, let the user register, send the data to server using xampp+php+mysql.
2. create a session like method that will save your detail in a variable (device memory) so that each time it will check user credential. if the user is logged in it will not ask to re-login.
3. while login user will enter id and password first time. send credential to server , check credential on database,if user exists with same detail. save detail in session method in device memory.
4. next time if user run the app check detail from the session variable.
5. You can also use device id and save it on server but if your app can be used by same user on other phone that there might be some problem.
for more detail
Android Hive login
Tutorial point Login