This feature is a nifty one to have if a few of your friends play Blur and you want to rub what you do in their face. First, head to Options in either Career or Multi-player, and you will see options to sync both your Twitter and Facebook accounts (whichever you prefer to enter, doesn't matter). If you've entered everything right, a dialogue will say so. Now you're ready to send your message out.
To share your info to the world via Facebook and Twitter, hit LB on any page and choose a statistic to share. The game will then show you what it will send out. Edit it if you wish, then press A to send. Do so, then *ding* 10G in the bank.
Alternative way (thanks Mister Spinger):
It also gives you the option to send out a message over XBL. Once I chose that option, and the stat I wanted to send out, the message window opened and the achievement popped. Then I just cancelled the message, no sense sharing my crappy stats with someone if I don't have to =)
Did I miss anything? If so, let me know in the comments.