RDS is not a database engine. It's a service that manages the infrastructure for you that's required to maintain a highly available and fault tolerant database. It supports a number of different engines such as MySQL as you mentioned. Please read the docs for more information.
You need to connect to your RDS MySQL instance the same way you would connect to any MySQL database. Using a library that supports MySQL, and using the hostname, username and password for your database.
However, it's probably not the best design to have phone clients connecting to your database remotely. The best thing to do would be to put a REST API on AWS that interfaces with your database.
Having n users connected to your database from each handset using your app is probably a bad idea. It means you need to have more power in your database, greatly hinders your scalability and makes things less secure as the database is exposed to the internet. With an API in front of it, you can build a much more fault tolerant, scalable and solution.
The "cloud way" to build mobile apps is to (within reason) build your application logic on the cloud and simply have your client code connect to your API. This way you can spread to more platforms (eg. IOS, Web) much more easily as you won't have to manage separate application level code for each platform. You'll just need to manage code that integrates with your already existing API.
Take a look at this whitepaper. Ignore the web server tier and focus on the App Server and Database tiers. This is probably the best design to go by.
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