Go to View > SPLIT > Code-Design, Split-Vertically (see screenshot).

Assuming your .dwt file is a correctly formed Template and free of code errors (denoted by a green checkmark), you should be able to edit in either Code or Design view panels.
A properly designed Template contains Editable Regions for content that changes on child pages. Something like this:
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<!-- TemplateBeginEditable name="doctitle" -->
<title>Unique Page Title</title>
<!-- TemplateEndEditable -->
<!--link to external CSS file-->
<link href="../css/my_styles.css" rel="stylesheet" type="text/css">
<!-- TemplateBeginEditable name="head" -->
<!-- TemplateEndEditable -->
</head>
<body>
<header>Content for sitewide header goes here</header>
<nav>
<a href="http://example.com"
>Example.com</a>
<a href="http://example.com"
>Example.com</a>
<a href="http://example.com"
>Example.com</a>
<a href="http://example.com"
>Example.com</a>
</nav>
<!-- TemplateBeginEditable name="EditRegionArticle" -->
<article>Content for unique article goes here. Very important for search engines.
</article>
<!-- TemplateEndEditable -->
<!-- TemplateBeginEditable name="EditRegionAside" -->
<aside>Content for unique aside Tag Goes Here</aside>
<!-- TemplateEndEditable -->
<footer>Content for sitewide footer Tag Goes Here</footer>
</body>
</html>
Hope that helps.