You could do this in two ways.
1) Leave the pages as separate pages in the WordPress dashboard and create a custom page template that lists those pages content. Assign this custom template to the homepage.
2) Move the content of those pages into the homepage editor.
Option 1:
A much cleaner option and allows you to revert to individual pages at a later stage. It also makes editing pages a lot easier.
Setup a custom page template, I'm going to call it page-home.php, but you can call it whatever you like.
You'll need to create this template inside your theme folder. The path (in a standard installation of WordPress) should be /wp-content/themes/your-theme/, where "your-theme" is the name of your theme.
NB: If you're theme is updated you will probably lose this template. To prevent this, I'd suggest creating a child theme.
It's probably easiest to copy the contents of page.php and paste it into your newly created page-home.php to retain theme markup. At the top of page-home.php insert the following.
<?php
/*
* Template Name: Home Page
*/
?>
Look for the default loop that most likely looks something like this.
<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
<!-- Loop HTML/PHP -->
<?php endwhile; endif; ?>
Now you want to replace the default loop with the following code.
<?php
$pages = get_pages( array(
'sort_column' => 'menu_order', // allows you to order pages using menu order under page attributes
'exclude' => 3, // the home page ID
) );
?>
<?php
foreach ( $pages as $page ) {
$content = $page->post_content;
if ( ! $content ) // Check for empty page
continue;
$content = apply_filters( 'the_content', $content );
?>
<div id="page-<?php echo $page->ID; ?>">
<?php echo $content; ?>
</div>
<?php
}
?>
Once you've saved this template in the theme, go edit your home page. (If it doesn't already exist, create one and go to your Dashboard > Settings > Reading, and change the Front page displays option to static page and select your newly created home page.) and select the template.
Option 1 Menu
Each section will have an ID that looks like this page-34 where 34 is the pages ID. If you're not sure how to find a page ID, check out this video.
Create the menu as you usually would under Appearance > Menus. Instead of inserting pages though, use links. For example let's say I want to add a page named Dummy with the ID of 34. I'd go to menus and switch to the Links dropdown. In the URL field enter "#page-34" and in the link text field, enter whatever you like, but mine would be "Dummy". Then click Add to Menu.
Rinse and repeat for all pages you'd like to add to the menu. Once the menu is saved you should have standard WordPress menu where each menu item links to the relevant section.
Option 2:
Edit the home page and switch to the text view of the WYSIWYG editor.
For each "page" add a div with a unique ID like this.
<div id="page-about">
<!-- about page content here -->
</div>
Insert the page content between those div tags. Repeat for every page you want to add to the home page. For example:
<div id="page-contact">
<!-- contact page content here -->
</div>
Option 2 Menu
Create the menu as you usually would under Appearance > Menus. Instead of inserting pages though, use links. To link to the about page section you'd add a new link with the URL set to "#page-about". To link to the contact page section add a new link with the URL set to "#page-contact". Rinse a repeat for all other pages.
