To add an embedded sign up form to your website you'll first need to get the embed code from Mailchimp which can be done by following this guide which outlines how to create the signup form, how to customize it, and how to get the embed code for your form.
Once you've got the embed code make sure you copy it down and keep it ready as we're now going to add it in the editor.
Select App Integrations
And then select Third-Party Integrations
From here click the Add a third party integration button and find Mailchimp in the popup that appears:
You should now see a field where you can enter the code from earlier:
After adding the code press back, this will take you back to your list of added integrations. Toggling the switch will enable the ability to add the form to your pages.
Navigate to the page you want to add the form, and click the add a section button. You will be able to see your form under the category "Section Integrations".
Once you've added it to the page that you want the form to appear on click publish and it will now appear on your live site.