How to map my php files as the files for pages

Use page templates, an overview can be found here: http://codex.wordpress.org/Page_Templates

Edit for those afraid of dying links:

A page template file should be placed in the theme folder, with any name you like. In its header, it should have

<?php
/*
 * Template Name: My Custom Page
 * Description: A Page Template with a darker design.
 */

// Code to display Page goes here...

In admin menu, each page will have the option to be assigned the template My Custom Page and this file will be used to show the page’s content. As a starting point, you could copy code from page.php or if that doesn’t exist, index.php