I discovered that it’s not super easy or intuitive to add a gfycat to Medium (something we’re working on) but in the meantime I did discover a way you can accomplish what I believe most people are looking for. Here’s how to add a gfycat to Medium so it looks like it’s embedded in your post. Create your draft and put whatever text you might want. Step one: Add the URL for the gfycat you are looknig to add. Please note it should appear exactly as follows substituting out the gfycat name. Meaning make sure the url is http://gfycat.com/<ThisIsYourGfycatName> Step two: Step three: The Magic. I hope that helps and is what people are looking for!
