AndroidManifest.xmlactivity_main.xmlMainActivity.java
<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="com.codinginflow.permissionrequestexample">

    <uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE"/>

    <application
        android:allowBackup="true"
        android:icon="@mipmap/ic_launcher"
        android:label="@string/app_name"
        android:roundIcon="@mipmap/ic_launcher_round"
        android:supportsRtl="true"
        android:theme="@style/AppTheme">
        <activity android:name=".MainActivity">
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />

                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
    </application>

</manifest>

<?xml version="1.0" encoding="utf-8"?>
<android.support.constraint.ConstraintLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context="com.codinginflow.permissionrequestexample.MainActivity">

    <Button
        android:id="@+id/button"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:text="Request Permission"
        app:layout_constraintBottom_toBottomOf="parent"
        app:layout_constraintLeft_toLeftOf="parent"
        app:layout_constraintRight_toRightOf="parent"
        app:layout_constraintTop_toTopOf="parent" />

</android.support.constraint.ConstraintLayout>

package com.codinginflow.permissionrequestexample;

import android.Manifest;
import android.content.DialogInterface;
import android.content.pm.PackageManager;
import android.support.annotation.NonNull;
import android.support.v4.app.ActivityCompat;
import android.support.v4.content.ContextCompat;
import android.support.v7.app.AlertDialog;
import android.support.v7.app.AppCompatActivity;
import android.os.Bundle;
import android.view.View;
import android.widget.Button;
import android.widget.Toast;

public class MainActivity extends AppCompatActivity {
    private int STORAGE_PERMISSION_CODE = 1;

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

        Button buttonRequest = findViewById(R.id.button);
        buttonRequest.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View v) {
                if (ContextCompat.checkSelfPermission(MainActivity.this,
                        Manifest.permission.READ_EXTERNAL_STORAGE) == PackageManager.PERMISSION_GRANTED) {
                    Toast.makeText(MainActivity.this, "You have already granted this permission!", 
                            Toast.LENGTH_SHORT).show();
                } else {
                    requestStoragePermission();
                }
            }
        });
    }

    private void requestStoragePermission() {
        if (ActivityCompat.shouldShowRequestPermissionRationale(this, 
                Manifest.permission.READ_EXTERNAL_STORAGE)) {

            new AlertDialog.Builder(this)
                    .setTitle("Permission needed")
                    .setMessage("This permission is needed because of this and that")
                    .setPositiveButton("ok", new DialogInterface.OnClickListener() {
                        @Override
                        public void onClick(DialogInterface dialog, int which) {
                            ActivityCompat.requestPermissions(MainActivity.this, 
                                    new String[] {Manifest.permission.READ_EXTERNAL_STORAGE}, STORAGE_PERMISSION_CODE);
                        }
                    })
                    .setNegativeButton("cancel", new DialogInterface.OnClickListener() {
                        @Override
                        public void onClick(DialogInterface dialog, int which) {
                            dialog.dismiss();
                        }
                    })
                    .create().show();

        } else {
            ActivityCompat.requestPermissions(this, 
                    new String[] {Manifest.permission.READ_EXTERNAL_STORAGE}, STORAGE_PERMISSION_CODE);
        }
    }

    @Override
    public void onRequestPermissionsResult(int requestCode, @NonNull String[] permissions, @NonNull int[] grantResults) {
        if (requestCode == STORAGE_PERMISSION_CODE)  {
            if (grantResults.length > 0 && grantResults[0] == PackageManager.PERMISSION_GRANTED) {
                Toast.makeText(this, "Permission GRANTED", Toast.LENGTH_SHORT).show();
            } else {
                Toast.makeText(this, "Permission DENIED", Toast.LENGTH_SHORT).show();
            }
        }
    }
}