I've created a leaflet map using maptiler.
It's created a leaflet HTML file, which links to PNG images on my desktop and displays the image.
How do I embed the map onto a blog such as tumblr?
Your HTML page is on a server (even if it's on your desktop) ? If not, you'll have to host it somewhere Tumblr/any other blog can reach.
Do not consider hosting it on your PC tho as you'll have to expose it publicly.
Once it has been done, just embeds an iframe in your blog page that will point to your leaflet HTML file. It will do it.