How would I go about copyrighting my app for release and beta testing?

Ideas themselves are not protectable. Expressions of ideas may be protected under copyright, and functional or aesthetic implementations of ideas may be protected under patent. Copyright protection attaches automatically, though in the context of software / code the protection is very thin. Apps - whether they are made available via closed / open beta or simply published on Google Play / iTunes - are generally protected by an End User License Agreement (EULA) by which the owner of the App and its content is granting users a limited license to do XYZ under terms which generally protect the owner in unilateral fashion. You won't be able to prevent a beta tester from stealing your idea, but you will be able to contractually prevent the user from engaging in a variety of adverse behavior. Further, though while software patents are particular squishy intellectual property assets, obtaining patent protection for what you are doing, if possible, is something you may attempt to enforce against others who are doing what your app does without authorization (e.g., without paying royalties). You should speak with local IP counsel about your App and lager business goals before any significant distribution.