activity_main.xmlDatePickerFragment.javaMainActivity.java
<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context="com.example.application.datepickerexample.MainActivity">

    <TextView
        android:id="@+id/textView"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_above="@id/button"
        android:layout_centerHorizontal="true"
        android:layout_marginBottom="28dp"
        android:text="date"
        android:textSize="30sp" />

    <Button
        android:id="@+id/button"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_centerHorizontal="true"
        android:layout_centerVertical="true"
        android:text="open date picker" />

</RelativeLayout>

package com.example.application.datepickerexample;

import android.app.DatePickerDialog;
import android.app.Dialog;
import android.os.Bundle;
import android.support.annotation.NonNull;
import android.support.v4.app.DialogFragment;

import java.util.Calendar;


public class DatePickerFragment extends DialogFragment {

    @NonNull
    @Override
    public Dialog onCreateDialog(Bundle savedInstanceState) {
        Calendar c = Calendar.getInstance();
        int year = c.get(Calendar.YEAR);
        int month = c.get(Calendar.MONTH);
        int day = c.get(Calendar.DAY_OF_MONTH);

        return new DatePickerDialog(getActivity(), (DatePickerDialog.OnDateSetListener) getActivity(), year, month, day);
    }
}

package com.example.application.datepickerexample;

import android.app.DatePickerDialog;
import android.support.v4.app.DialogFragment;
import android.support.v7.app.AppCompatActivity;
import android.os.Bundle;
import android.view.View;
import android.widget.Button;
import android.widget.DatePicker;
import android.widget.TextView;

import java.text.DateFormat;
import java.util.Calendar;

public class MainActivity extends AppCompatActivity implements DatePickerDialog.OnDateSetListener {

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

        Button button = (Button) findViewById(R.id.button);
        button.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View v) {
                DialogFragment datePicker = new DatePickerFragment();
                datePicker.show(getSupportFragmentManager(), "date picker");
            }
        });
    }

    @Override
    public void onDateSet(DatePicker view, int year, int month, int dayOfMonth) {
        Calendar c = Calendar.getInstance();
        c.set(Calendar.YEAR, year);
        c.set(Calendar.MONTH, month);
        c.set(Calendar.DAY_OF_MONTH, dayOfMonth);
        String currentDateString = DateFormat.getDateInstance(DateFormat.FULL).format(c.getTime());

        TextView textView = (TextView) findViewById(R.id.textView);
        textView.setText(currentDateString);
    }
}