UPDATE: July 10, Instagram releases new embed feature for the desktop web browser version!
Currently, as of July 7, 2013, Instagram does not have a simple method for users to grab their videos and embed them into a blog post or a web page.
Now, when you visit an Instagram user page on your desktop web browser, you’ll see a new share button on the right side of your photo (just under the comments button). Click the button to see the embed code. Copy the block of text it offers and paste it into your blog, website or article. When you hit publish, the photo or video will appear. Nice!
Embedded photo or videos appear with the Instagram username of the owner, and clicking on the Instagram logo will take people to your page on Instagram.com where they can discover more of your photos and videos.