It's not currently possible to download or export individual mods made on LearnToMod.
(It's not possible to get a .jar file)
How to Copy and Paste Code
Each badge or editor screen has a small gray JS button that allows you to view the code in JavaScript format. (located near the Simulator button). To copy the code, you'll have to do so from the freeplay modding section. At the top of the page of the freeplay modding section there's a drop down menu -- select copy. Then you can paste the code in a plain .txt document. What you do with it next is up to you.