There are, in fact, three ways to claim Google Authorship, but if you have a WordPress.com blog there is only one way.
The other ways require you to have an email address that is the same as your blog’s URL or domain name, and if you have a WordPress.com blog you can’t use wordpress.com because you don’t own it! And you can’t upload plugins into a WordPress.com blog so that way won’t work either.
So the only method available is what I have presented in this infographic below:
And of course I’ve provided you with some code you could paste into your own posts if you want to share this infographic with your readers. Remember to put it into the Text mode of your Edit Post page.
The only complicated bits are probably finding the full URL of your Google+ account with the numbers and not the vanity URL, and placing the special code into your About page that needs to connect with your Google+ account.
Your numbered Google+ URL can be found by mousing over the avatar in your ‘tag’ in your Google+ About section. And the code needs to be added while in the Text mode when you edit your About page.
This may seem to be a lot to cope with, especially if you are non-technical, but I assure you it would make a big difference to your writing and how it is perceived on the web if you were able to complete this task and successfully claim Google Authorship.