You will need the Full Write Service Plans permission or be an organizer on the plan to perform this action..
Navigate to the service plan you want to embed and click on the Embed button in the right column to access the embed code you can paste on your web page. The embedded plan will use the same sharing options that are set for that plan. See this article for more information on enabling public sharing.
Important: Make sure the plan is set to share publicly as the Embed button will not appear otherwise.