Simple script to add a smooth scrolling to your site wrote in vanilla JavaScript.
Just download and add to your site like normal JS script. For example:
<script src="./yourFolderWithJS/script.js" type="text/javascript"></script>
Of course there is no problem with renaming this file.
Add class="js-nav" to parent of elements you want to run this script when clicked. You can have many menus if you want, but every of them need to have class="js-nav". Links must be in 'href' of element 'a' and point to id located on site. For example:
<ul class="js-nav">
<li><a href="#home">Home</a></li>
<li><a href="#about">About me</a></li>
<li><a href="#contact">Contact me</a></li>
</ul>
<header id="home"></header>
<section id="about"></section>
<section id="contact"></section>
That's first version of script so it could work not exactly predictable, but I'm working on it, so be prepared for next versions with brand new bugs.
It's free to use and to change whatever you want.