The way I would do it is, I would first add three methods similar to this one (each for a single fragment. Replace the layout name and the fragment object to the appropriate fragment that is being switched to):

public void switchToFragment1() {
    FragmentManager manager = getSupportFragmentManager();
    manager.beginTransaction().replace(R.id.your_fragment_layout_name, new Fragment1()).commit();
}

So your switch statement would end up looking like this:

        switch (item.getItemId()) {
            case R.id.navigation_home:
                mTextMessage.setText(R.string.title_home);
                switchToFragment1();
                break;

            case R.id.navigation_dashboard:
                mTextMessage.setText(R.string.title_dashboard);                    
                switchToFragment2();
                break;

            case R.id.navigation_notifications:
                mTextMessage.setText(R.string.title_notifications);                     
                switchToFragment3();
                break;
        }

As for switching the fragments by swiping to the sides, I believe you would need a ViewPager.

It's pretty "simple".

1. Create your Fragments. Let's say we want 3 fragments; FragmentA, FragmentB and FragmentC with FragmentA being the first Fragment we want on the BottomNavigationView.

2. In your Activity, go to the onNavigationItemSelected method and change the content to this:

    private BottomNavigationView.OnNavigationItemSelectedListener  
      mOnNavigationItemSelectedListener
          = new BottomNavigationView.OnNavigationItemSelectedListener(){
   
      @Override
      public boolean onNavigationItemSelected(@NonNull MenuItem item) {
   
       switch (item.getItemId()) {
           case R.id.frag_a:
               currentFragment = new FragmentA();
               ft = getSupportFragmentManager().beginTransaction();
               ft.replace(R.id.content, currentFragment);
               ft.commit();
               return true;
           case R.id.frag_b:
               currentFragment = new FragmentB();
               ft = getSupportFragmentManager().beginTransaction();
               ft.replace(R.id.content, currentFragment);
               ft.commit();
               return true;
           case R.id.frag_c:
               currentFragment = new FragmentC();
               ft = getSupportFragmentManager().beginTransaction();
               ft.replace(R.id.content, currentFragment);
               ft.commit();
               return true;
       }
   
       return false;
    }
   
   };
   

3. In your onCreate()method, do this:

     @Override
     protected void onCreate(Bundle savedInstanceState) {
       super.onCreate(savedInstanceState);
       setContentView(R.layout.activity_client_profile);
       ft = getSupportFragmentManager().beginTransaction();
       currentFragment = new FragmentA();
       ft.replace(R.id.content, currentFragment);
       ft.commit();
   
       BottomNavigationView navigation = (BottomNavigationView)  
       findViewById(R.id.navigation); navigation.setOnNavigationItemSelectedListener(mOnNavigationItemSelectedListener);
     }
   

If you do not add FragmentA in the onCreate(), the activity is blank when you first launch it.

If you are wondering what R.id.content refers to, it is the Id of the Framelayout in your activity's layout. It initially contains a TextView, delete the TextView so it looks like this:

<FrameLayout
    android:id="@+id/content"
    android:layout_width="match_parent"
    android:layout_height="0dp"
    android:layout_weight="1"/>

Finally, ft and currentFragment are defined like this:

Fragment currentFragment = null;
FragmentTransaction ft;

Not sure about elegance, but this works.

The best way is to use a ViewPager with a FragmentPagerAdapter. Since it cashes the fragments inside it. Use setOnNavigationItemSelectedListener with the BottomNavigationView to listen for the user's clicks. And use viewPager.setCurrentItem(..) to move between pages.

Creating a new fragment everytime the user clicks on an item in the bottom navigation view isn't a good solution (especially when the user clicks on the item of the screen that he is currently at, the solution above will create a new fragment even for this case)