301 redirects in Headway based WordPress Site

First of all, Headway is not the issue, if Headway itself doesn’t deal with any kind of 301 redirect.

And answer to the question is:
After having the folder in action if you change the “WordPress Address (URL)” and “Site Address (URL)” in your /wp-admin/options-general.php (Admin » Settings » General) to the new address like:

http://example.com/blog/

Then the whole site will work with the new URL. (After the change you will just need to reenter the admin panel once – and that’s all)

So, the first issue is solved.

But there could be an underlying issue with hard-coded inner links used in a blog. Suppose you linked one of your post with a simple text link (<a href="http://example.com/blog-post-name-1">My blog post 1</a>) — after the folder URL such links will generate 404, and that will be the problem. A similar issue is cited in one of my Question:

So in that case you will need a .htaccess 301 redirection. But most of us are not so expert about .htaccess, so there are some plugins, can help us in our way.

Yoast have a good URL redirection plugin that can assist you in achieving this. And there are more on this category:

With your input they will write .htaccess with right codes on your behalf.