It's well known that social networks track your surfing behavior on any web site that embeds their buttons and/or widgets (e.g. the facebook "like" button). It's a lesser known fact that logging out, or even deleting your cookies won't necessarily help (part 1, part 2, see for yourself).
This is not only true for social networks. Other 3rd party sites like ad networks (and even google analytics) also use such techniques. What makes social networks special is that even well meaning webmasters (personal blogs, voluntary orgs, etc.) who would rather not enter this ugly game, are being cornered into using these intrusive widgets if they want their readers (that's you) to have an easy, 1-click way to spread the word about their content.
The idea behind the "+2" concept is that unless you actively decide to recommend a page via a social network, there's no reason to display that network's like/tweet/+1 button and help said social network track your visit. This is why the Social Share Privacy widget (aka "+2 widget") displays "inactive versions" of those buttons instead (see example on this page).
The first click "activates" the button by fetching the actual widget from the social network's site and displaying it instead of its "inactive version". The second click does the actual job of liking/tweeting/+ing
Only after the first click, your visit can (and probably will) be tracked by the social network, but that's OK because the fact that you've visited the page is no longer a secret (you're about to publicize it anyway). Also note that other social networks don't get to track your visit (unless you decide to activate their buttons as well).
Protect the privacy of your users. Install the social share privacy (aka "+2") widget.
If you're not part of the adsense game, also consider avoiding google analytics as well, by installing your own web analytics software. On the other hand, even if you can't (or won't) avoid google analytics, bear in mind that using the "+2" widget still protects your users from some of the tracking they're subjected to.
The original Social Share Privacy (aka "+2") widget was developed and is maintained by the German magazine Heise Online. It's distributed under the MIT license. The GUI and documentation are in the German language. You can read more about it here.
This version adds internalization to English and is distributed under the same license.