It’s easy. WordPress has already this functionality, you just have to know where to enable this feature from the menu’s settings page.
First of all, you need to create your own menu. When you click on one of the items, you’ll see few text fields where you will be able to change the title and attribute of the item.
To enable the CSS class, click on the Screen Options button on the top right side of your screen. Then, tick on CSS Classes option. Once you’ve enabled it, a new text field will be added. Then, just put any custom classes you’ve declared in your style.css.
In one of my projects for a client, I need to create a colorful menu. The best way to do it is by using a custom class for every item in the menu. And here’s the result: