There are few Shopify apps that do a great job providing “You are X amount away from free shipping”, but in case you don't want to install another app, there is a way of adding a small snippet of javascript that will do the same thing.

Finding the event

Most of the themes have the onCartUpdate event that will trigger some actions on the javascript side to update some parts of a page (eg cart counter).
This can be found at Assets folder in your Shopify theme.
Open file ajax-cart.js.liquid or similiar (main.js.liquid) and search for function onCartUpdate. Found it? Great!

Creating a function

Let’s create our function which will be called on onCartUpdate…