You need to follow certain steps

To replicate the newsletter form as this : http://bsf.io/gdwr1

Step 1: Install the mailchimp plugin: https://wordpress.org/plugins/mailchimp-for-wp/

Step 2: Create your account in Mailchimp.com and create your API key and enter that API key to get connected with mailchimp plugin, here is the screenshot: http://bsf.io/dmxcg

Once you save the changes your status would be connected after sometime: http://bsf.io/8t0a4

Step 3: Go to form option and put the below code in the form markup area: http://bsf.io/flr9s

Step 4: Then go to the appearance–>widget and drag the Mailchimp widget to your desired footer area: http://bsf.io/j4b76

Hope this helps!