¿Cómo transferir algunos datos a otro fragmento?

Para extender aún más la respuesta anterior, como decía Ankit, para objetos complejos es necesario implementar Serializable. Por ejemplo, para el objeto simple:

public class MyClass implements Serializable {
    private static final long serialVersionUID = -2163051469151804394L;
    private int id;
    private String created;
}

En ti defragment:

Bundle args = new Bundle();
args.putSerializable(TAG_MY_CLASS, myClass);
Fragment toFragment = new ToFragment();
toFragment.setArguments(args);
getFragmentManager()
    .beginTransaction()
    .replace(R.id.body, toFragment, TAG_TO_FRAGMENT)
    .addToBackStack(TAG_TO_FRAGMENT).commit();

En tu ToFragment:

@Override
public View onCreateView(LayoutInflater inflater, ViewGroup container,
            Bundle savedInstanceState) {

    Bundle args = getArguments();
    MyClass myClass = (MyClass) args
        .getSerializable(TAG_MY_CLASS);

GetArguments() devuelve null porque "Its no obtiene nada"

Pruebe este código para manejar esta situación

if(getArguments()!=null)
{
int myInt = getArguments().getInt(key, defaultValue);
}

Código completo de pasar datos usando fragmento a fragmento

Fragment fragment = new Fragment(); // replace your custom fragment class 
Bundle bundle = new Bundle();
FragmentTransaction fragmentTransaction = getSupportFragmentManager().beginTransaction();
                bundle.putString("key","value"); // use as per your need
                fragment.setArguments(bundle);
                fragmentTransaction.addToBackStack(null);
                fragmentTransaction.replace(viewID,fragment);
                fragmentTransaction.commit();

En la clase de fragmento personalizado

Bundle mBundle = new Bundle();
mBundle = getArguments();
mBundle.getString(key);  // key must be same which was given in first fragment

Solo para extender las respuestas anteriores, podría ayudar a alguien. Si su getArguments() devuelve null, póngalo en el método onCreate() y no en el constructor de su fragmento:

@Override
public void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    int index = getArguments().getInt("index");
}

            First Fragment Sending String To Next Fragment
            public class MainActivity extends AppCompatActivity {
                    private Button Add;
                    private EditText edt;
                    FragmentManager fragmentManager;
                    FragClass1 fragClass1;


                    @Override
                    protected void onCreate(Bundle savedInstanceState) {
                        super.onCreate(savedInstanceState);
                        setContentView(R.layout.activity_main);
                        Add= (Button) findViewById(R.id.BtnNext);
                        edt= (EditText) findViewById(R.id.editText);

                        Add.setOnClickListener(new View.OnClickListener() {
                            @Override
                            public void onClick(View v) {
                                fragClass1=new FragClass1();
                                Bundle bundle=new Bundle();

                                fragmentManager=getSupportFragmentManager();
                                fragClass1.setArguments(bundle);
                                bundle.putString("hello",edt.getText().toString());
                                FragmentTransaction fragmentTransaction=fragmentManager.beginTransaction();
                                fragmentTransaction.add(R.id.activity_main,fragClass1,"");
                                fragmentTransaction.addToBackStack(null);
                                fragmentTransaction.commit();

                            }
                        });
                    }
                }
         Next Fragment to fetch the string.
            public class FragClass1 extends Fragment {
                  EditText showFrag1;


                    @Nullable
                    @Override
                    public View onCreateView(LayoutInflater inflater, @Nullable ViewGroup container, @Nullable Bundle savedInstanceState) {

                        View view=inflater.inflate(R.layout.lay_frag1,null);
                        showFrag1= (EditText) view.findViewById(R.id.edtText);
                        Bundle bundle=getArguments();
                        String a=getArguments().getString("hello");//Use This or The Below Commented Code
                        showFrag1.setText(a);
                        //showFrag1.setText(String.valueOf(bundle.getString("hello")));
                        return view;
                    }
                }
    I used Frame Layout easy to use.
    Don't Forget to Add Background color or else fragment will overlap.
This is for First Fragment.
    <FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
        xmlns:tools="http://schemas.android.com/tools"
        android:id="@+id/activity_main"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        android:paddingBottom="@dimen/activity_vertical_margin"
        android:paddingLeft="@dimen/activity_horizontal_margin"
        android:paddingRight="@dimen/activity_horizontal_margin"
        android:paddingTop="@dimen/activity_vertical_margin"
        android:background="@color/colorPrimary"
        tools:context="com.example.sumedh.fragmentpractice1.MainActivity">

        <EditText
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:id="@+id/editText" />
        <Button
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:layout_gravity="center"
            android:id="@+id/BtnNext"/>
    </FrameLayout>


Xml for Next Fragment.
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:orientation="vertical" android:layout_width="match_parent"
   android:background="@color/colorAccent"
    android:layout_height="match_parent">
    <EditText
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:id="@+id/edtText"/>

</LinearLayout>

Tu fragmento de entrada

public class SecondFragment extends Fragment  {


    EditText etext;
    Button btn;
    String etex;
    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState) {
        View v = inflater.inflate(R.layout.secondfragment, container, false);
        etext = (EditText) v.findViewById(R.id.editText4);
        btn = (Button) v.findViewById(R.id.button);
        btn.setOnClickListener(mClickListener);
        return v;
    }

    View.OnClickListener mClickListener = new View.OnClickListener() {
        @Override
        public void onClick(View v) {


            etex = etext.getText().toString();
            FragmentTransaction transection = getFragmentManager().beginTransaction();
            Viewfragment mfragment = new Viewfragment();
            //using Bundle to send data
            Bundle bundle = new Bundle();
            bundle.putString("textbox", etex);
            mfragment.setArguments(bundle); //data being send to SecondFragment
            transection.replace(R.id.frame, mfragment);
            transection.isAddToBackStackAllowed();
            transection.addToBackStack(null);
            transection.commit();

        }
    };



}

Tu fragmento de vista

public class Viewfragment extends Fragment {

    TextView txtv;
    public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState) {
        View v = inflater.inflate(R.layout.viewfrag,container,false);
        txtv = (TextView)  v.findViewById(R.id.textView4);
        Bundle bundle=getArguments();
        txtv.setText(String.valueOf(bundle.getString("textbox")));
        return v;
    }


}