This code snippet does what you need, I've tested it. Suppose for the example you want the user to be able to switch language through a menu from your main activity. You can do it through saving a language flag as a user preference and check it on "onCreate()" and on "onConfigurationChanged()" as follows:
    public class MainActivity extends Activity {
SharedPreferences mPrefs1;
@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    mPrefs1 = PreferenceManager.getDefaultSharedPreferences(this);
    String languageToLoad = mPrefs1.getString("languagePref", Locale.getDefault().getLanguage());
    Locale locale = new Locale(languageToLoad); 
    Locale.setDefault(locale);
    Configuration config = new Configuration();
    config.locale = locale;
    getBaseContext().getResources().updateConfiguration(config,getBaseContext().getResources().getDisplayMetrics());
    setContentView(R.layout.activity_main);
}
@Override
public void onConfigurationChanged(Configuration newConfig) {
  super.onConfigurationChanged(newConfig);
    mPrefs1 = PreferenceManager.getDefaultSharedPreferences(this);
    String languageToLoad = mPrefs1.getString("languagePref", Locale.getDefault().getLanguage());
    Locale locale = new Locale(languageToLoad); 
    Locale.setDefault(locale);
    Configuration config = new Configuration();
    config.locale = locale;
    getBaseContext().getResources().updateConfiguration(config,getBaseContext().getResources().getDisplayMetrics());
    setContentView(R.layout.activity_main);
}
// Declaring the Menu options
@Override
public boolean onCreateOptionsMenu(Menu menu)
{       
    MenuInflater inflater = getMenuInflater();
    inflater.inflate(R.menu.main_menu, menu);
    return true;
}
//handle menu item selection
public boolean onOptionsItemSelected(MenuItem item)
{
  switch (item.getItemId()) {
    case R.id.menu_switch_language:
        String languageToLoad  = getResources().getString(R.string.switch_language);
        mPrefs1 = PreferenceManager.getDefaultSharedPreferences(this);
        SharedPreferences.Editor editor = mPrefs1.edit();
        editor.putString("languagePref", languageToLoad);
        editor.commit(); // Very important to save the preference                      
        finish();
        startActivity(getIntent());
        return true;
    default:
        return super.onOptionsItemSelected(item);
  }
}   
}