More and more weight is being given to good online authors by Google and as such, it would be wasteful for an author or publisher not to set it up. The idea is that writers that produce good material, that is well-written, relevant and useful to their audience, rise to the top of the SERPs as they are a 'trusted' author.
Any business looking to set up some kind of authoritative voice or become a thought leader in their industry should have Google Authorship set up. It also means that the search results for an article will show a headshot of the author, alongside their name and a snippet of content.
To get started with Authorship, you'll first need to set up a Google+ profile and if you're a publisher, you should also set up a company page. This is because publishers can benefit from the Authorship scheme by linking what they publish to their G+ company page, increasing the visibility and authority of their content.
Fill in the appropriate sections of your profile and ensure that you choose a good headshot for your profile picture, as this is what will appear in snippets, as above.
Once you have done this, add links to sites that you're a contributor to in the About section:
In the top editing box you put a label, so the name of the site or a description, in the second box you put the URL to the site. If you have a dedicated author page, then put in the URL for that.
Do this for all of the sites that you contribute to. Note that this doesn't add the author markup so that you will appear in snippets though. Make sure that your G+ profile name is exactly as it appears in your articles and blogs and that the posts themselves have your byline, ie: By Joe Bloggs.
This will bring up relevant posts in your Author Stats, but won't add your picture and relevant snippet information in search results.
Once you have followed the steps above, you should (if you haven't already) sign up for Authorship. Ideally, you want to be able to link everything you write to your G+ account and have it verified.
There are two ways in which this can be carried out.
1. Adding an email address for the domain that you're writing for
This is the easy way. Ask sites that you write for if they are willing to set you up with an email address on their domain. In the 'About' section, add the email address to your G+ account in the work section, you can do this through the Authorship signup page as well.
2. Adding the rel=author tag
This is a little more difficult and can be impossible if you have no access to the domain. However, it can be placed in your author bio for sites that you guest post on, or are a regular contributor.
Assuming you're not using it in one bio, create a link to your G+ profile from your webpage which has the content written by you on it.
<a target="_blank" href="[profile_url]?rel=author">Google</a>
Replace the [profile_url] with your G+ profile URL:
<a target="_blank" href="https://plus.google.com/u/0/109822713436643034257?rel=author">Google</a>
Add a link on your G+ profile in the contributors section and save and that's it, your content for that URL is verified as being written by you. If this is to go in the bio of the content, then link to your G+ profile in the same manner.
If there are a lot of legacy sites that you write for, then you may still be recognised as the author as long as the work has your byline on the same page. However, you won't be verified as the author and so rich snippets with your photo and a link to more of your work won't appear.
Checking For Verification
You can check to see if you're recognised as the author using the structured data tool from Google. To do this you will need to collect the URLs that you want to check first and then enter them (one at a time) into the URL box.
Hit the preview button and it will tell you if you are the verified author for the page. If not, then ask the site owner to add the rel=author tag or add you to the domain with an email address.
As I said, you can still be associated with content even if you're not verified and you can keep your eye on how your posts are doing using the Webmaster Tools Author Stats. This shows you which posts are performing well, the CTR and how many views and impressions the post has had.
Whilst the tool does say that this is for those sites that have you as the verified author, many of the sites that I have written for in the past have neither used the markup, or added an email address for me, so many of those that appear in the stats are verified from my byline alone. However, I wouldn't recommend you take that route, getting the tag and rich snippets should be your aim as often as possible.
The Rel=publisher Tag
Whilst this isn't as powerful as Authorship as yet, it works in just the same way and can help with branding, as your company logo will appear in search results alongside content. To make a business page, just scroll to the bottom of the navigation menu until you see the more button.
Another button will appear called pages, choose this and a business category and fill out all of the necessary information. Rather than your G+ profile URL, you want to use the business page URL so make a note of it.
Add the rel=publisher tag to the home page of your website:
<link rel=publisher href="https://plus.google.com/202020202020202020202">
Note that the code should be in the head section of the home page, in between the head tags. Make sure that you also add a +1 button to the website, with your business page ID linked to it.
You can get WordPress plugins that can make both of these processes a lot easier. Make sure that you edit the business page too; in the links section add the URL to your homepage and save.
You will also need to verify that you own the site with Google using Webmaster Tools, if you haven't already done this for advertising or Analytics.
That's all that you need to do to set up Authorship! If, like me, you write for a lot of different sites, then make sure that you try to address any legacy content and if you can't, then just add to contributor list and choose 'past'.