To allow your fans and customers to subscribe direct to your mailing list you can add an embed to your home page, or make a dedicated mailing list sign-up page.
How to set up
Pages > Create Page
To add to your home page or other existing page, go that that page from the Pages list.
Add a code module
Add Module > Code
Paste embed code
Find the HTML embed code from your mail client and copy and paste it in to the Code text box.
Add descriptive / help text
To include any additional information about your mailing list and marketing add a Text module. This module can have a heading and body text, and can be formatted to include bold text, links and more.
Add Module > Text
<script> section of the embed. The form should still submit to the mail client as expected.
Display as pop-up
Mailchimp and ActiveCampaign both have an option to show the sign up form as a pop-up. You can set this up in the same way as a normal form embed. You should have the Code module containing the form to be at the top of the list of page modules. This is needed as the page loads modules in as you scroll, so the popup would only triggered after scrolling; setting the module to be at the top of the page means the popup appears when expected.