To include a newsletter subscription form in your theme, you just need to create an HTML form with its action attribute set to /newsletter-subscribe
Within this form you should have an input of type text with a name attribute set to to email
An example is shown below.
<form action="/newsletter-subscribe" method="post"> <input type="text" name="email"> <button type="submit">subscribe</button> </form>
Once the form has been submitted the user is redirected to the newsletter-subscription view.
Subscriptions to your newsletter are added to your account, read more here.