Thanks for your question! Check out these great posts that @Samantha_O wrote up on our Signup Form that you can add to your website below.
Get the Embed Code for your Sign Up Forms!
Part 2 - Updating the Embeddable Form
These should help you with getting the code from Constant Contact. We do not know how to insert it into your website. You'll want to contact your website developer for that.
Hope that helps!