How to create users in/for apps

I have a question that probably has a straight forward answer, but I am asking here to make sure.

If I want to develop an app with users (e.g. Snapchat, Wordfeud etc.), how do I do it? Do I have to use a database of some kind? The users will not have much information stored to them, say nothing more than a username and a score collection.

Can I do this without using databases? And how do I even set up an app for having users?