Tom,
The most common solution for this problem is:
1) Your application get data via a webservice in your server. You can use Soap solution based on XML communication, or simple REST access (simple http request in GET or POST method) and use your own choice: XML or JSON.
Today, there is a lot of solution based on REST GET/POST with JSON file communication.
2) After, if you want that your application can turn in offline mode or just be more reactive, you can store old loaded data by webservice in local database.
For this, in Android you can use direct access to sqlite database, and in iOs, you can use the CoreData api.
Hope it help you.
Fabecc.