First you need to define the button inside a <form> tag in the website template XML, e.g.

<form action="/my_new_controller" method="post">
    <!-- put other forms field here if you need to pass info to controller -->
    <button type="submit" class="btn">Call a controller</button>
</form>

Clicking the  button submits the form and calls the controller at www.myodoosite.com/my_new_controller. You can define the controller in python with something like this:

class website_account(http.Controller):

     @http.route(['/my_new_controller'], type='http', auth='public', website=True) 
     def my_controller_method(self, redirect=None, **post):
         # Put your backend operations here, e.g.
         # sale_model = request.env['sale.order']
         # sale_model.create({...})

         # After you're done, use either request.render() or request.redirect() to show
         # a different page to the user. You can check out the website_portal module for examples.