This is a very broad question. Perhaps a community wiki exists already with an answer for it. Anyways, here is a collection of resources related to secure storage in Android that should be helpful:
- Android training: http://developer.android.com/training/articles/security-tips.html
- Credential storage API: http://nelenkov.blogspot.jp/2012/05/storing-application-secrets-in-androids.html and http://nelenkov.blogspot.no/2013/08/credential-storage-enhancements-android-43.html
- You can use the Account Manager for accounts and add features and properties to it to keep custom data:
- http://developer.android.com/training/sync-adapters/creating-authenticator.html
- http://developer.android.com/reference/android/accounts/AccountManager.html
- https://github.com/android/platform_development/tree/master/samples/SampleSyncAdapter
- http://nelenkov.blogspot.no/2012/11/sso-using-account-manager.html
- http://udinic.wordpress.com/2013/04/24/write-your-own-android-authenticator/
- https://groups.google.com/forum/#!topic/android-developers/Vubkbfqimm8
- In general you should check out Nikolay Elenkov's blog with lot's of good articles on Android and security: http://nelenkov.blogspot.no/