I can definitely help you with inserting a sign up link or button in your email. I would like to mention though that this forum is for people who are integrating with Constant Contact using our API's. You may find that it is more helpful to contact our support channels by either phone at 866-289-2101, emailing us here, or customer chat.
Adding a link to your email does depend on what email client you are using. Some email clients allow HTML to be entered in easily, and others may not have this functionality. If you have an email client that allows HTML to be used, you can log into your account and go to the contacts tab and click on Join My Mailing List. The first step has you generate HTML code, which you can select a button and then paste the code into the email client signature section.
If you do not have an easy way to insert the HTML code, we do have various FAQs that show you how to insert a sign up link in your signature. Here is some examples for Outlook, Apple Mail, and Gmail.