This will cost you about $20, because you’ll need to buy a domain.
I am not particularly knowledgeable when it comes to  networking, DNS, or the ins and outs of CloudFlare, so if you’re worried about your blog in anyway, please don’t do it, or look into the possible hosting problems it could cause if it goes wrong.

Here’s how to do it:

1. Log in to your blog
2. Go to Store on the left-hand side-bar menu:

Then choose “Domains” from the menu that pops up

3. Buy a domain name, and choose the mapping option too (unless you know how to do it yourself, or do it cheaper)

4.  Sign up for a free version of CloudFare, at CloudFare.com

5. Under the “Websites” tab, click “Add Website”:

6. Once you’ve added your website, from the homepage, click the little ‘cog’ icon on the right hand side to bring up the drop down menu

7. Select DNS Settings

8. Change your DNS so that the first CNAME has a value/alias of lb.wordpress.com and make sure the cloud icon on the right is orange (click it if it isn’t).

9. Within 24 hours, you should be given to “name servers” like those shown on the top right here. These are displayed on the top right of the DNS settings page

10. Go back to the dashboard of your wordpress blog.
On the left side-bar menu, go to Store – Domains
Below your domains, you should see a drop down menu
Choose “Make Change to your Domains”
Copy your customer number (you’ll need this to log-in shortly)
Change your password to something you’ll remember in a minute’s time
Then click “Manage Your Domains” in the blue text at the bottom

11. Log in to the Domain DNS manager platform:

12. Tick the box on the left next to your domain name.
The click the second icon from the left on the top – Nameservers
Then click “Set NameServers”

13. Make sure “Custom” is checked
Then delete your current Name servers, and add those that CloudFare have provided:

14. This bit takes ages to sort out.  It took about 2 days for my nameservers to change over, and I received an email when they did.
When this happens, log in to CloudFare, choose “Apps” from the homepage

15. Turn on Google Analytics on the Apps page of CloudFare

16. Wait another 24 hours and log into Google Analytics. You should start seeing some data

Thanks to Pete & Emma for helping me to do this on my blog