xml of the Dialog:

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="<http://schemas.android.com/apk/res/android>"
    android:orientation="vertical" android:layout_width="match_parent"
    android:layout_height="match_parent">

    <DatePicker
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:id="@+id/datePicker"
        android:layout_gravity="center_horizontal"
        android:calendarViewShown="false"/>

    <Button
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:text="ACCEPT"
        android:id="@+id/buttonAccept" />

</LinearLayout>

Dialog Class:

public class ChooseDate extends DialogFragment implements View.OnClickListener {

    private DatePicker datePicker;
    private Button acceptButton;

    private boolean isDateSetted = false;
    private int year;
    private int month;
    private int day;

    private DateListener listener;

    public interface DateListener {
        onDateSelected(int year, int month, int day);
    }

    public ChooseDate(){}

    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                             Bundle savedInstanceState) {
        View rootView = inflater.inflate(R.layout.dialog_year_picker, container);

        getDialog().setTitle(getResources().getString("TITLE"));

        datePicker = (DatePicker) rootView.findViewById(R.id.datePicker);
        acceptButton = (Button) rootView.findViewById(R.id.buttonAccept);
        acceptButton.setOnClickListener(this);

        if (isDateSetted) {
            datePicker.updateDate(year, month, day);
        }

        return rootView;
    }

    @Override
    public void onClick(View v) {
        switch(v.getId()){
            case R.id.buttonAccept:
                int year = datePicker.getYear();
                int month = datePicker.getMonth() + 1; // months start in 0
                int day = datePicker.getDayOfMonth();
                
                listener.onDateSelected(year, month, day);
                break;
        }
        this.dismiss();
    }

    @Override
    public void onAttach(Context context) {
        super.onAttach(context);
        listener = (DateListener) context;
    }

    public void setDate(int year, int month, int day) {

        this.year = year;
        this.month = month;
        this.day = day;
        this.isDateSetted = true;
    }

}

Activity calling the dialog:

public class MainActivity extends AppCompatActivity implements ChooseDate.DateListener{

    private int year;
    private int month;
    private int day;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        
        private void showDateDialog();
    }

    private void showDateDialog(){
        ChooseDate pickDialog = new ChooseDate();
        // We could set a date
        //  pickDialog.setDate(23, 10, 2016);
        pickDialog.show(getFragmentManager(), "");
    }

    @Override
    onDateSelected(int year, int month, int day){
        this.day = day;
        this.month = month;
        this.year = year;
    }
}