Adding a Thunderforest tile layer in Leaflet is straightforward and doesn’t need many lines of code. Here is the code to describe a layer:
Adding a Thunderforest map layer
You can of course customise the URL depending on which of our different map styles you want to use.
Here, in slightly more detail, is an example of how to include a leaflet-based map into your page.
For more details on Leaflet, see http://leafletjs.com/