Facer Spacer in the comments section below has suggested a direct link Embed Instagram that you can use to generate the embed code for your website in a straightforward manner instead of going through multiple steps. Do check it out.
The older blog post follows…
How we take for granted embedding YouTube videos into our webpages and blog posts. The service provides you a simplified code that you can easily copy/paste. But what about other services? Your favorite photo hosting service Instagram recently launched its video feature where you can also upload videos (a la Vine). This is all good. But how do you embed one of the Instagram videos into your webpage or blog post if you want to share it with a larger audience? Remember that Instagram stuff can only be shared via your mobile phone.
This Mashable blog post gives you a step-by-step guide on how to achieve this task.