Usually the service you use for newsletters (Mail Chimp, Constant Contact etc..) give you the HTML for their forms, which you can then add into the content area of the Page Header.
You would have to use CSS media queries. If you’re getting the HTML from a place like Mail Chimp or Constant Contact, they might have a responsive version of the form.
Thanks Tom. I am using MailRelay. They do not have CSS-based forms. Any sample code I can get. As of now, my site is looking good only in browsers. Thanks!