How does one share stuff on Google+ using buttons like the ones Facebook / Twitter have

A standard, simple hyperlink way of +1ing something (and sharing to Google+) is now making the rounds on blogs (couldn't find an official source, so it may still be undocumented):

https://plusone.google.com/_/+1/confirm?hl=en&url=%URL

Replace %URL with the URL. This is what shows up in the Google+ stream:

I don't think it is possible to determine the identities of the people who gave a Google +1 to a website or URL, whether on your own website or one that you don't control. This wasn't announced until 27 Jun 2012 by Google, a long time after you asked your question! Now Google policy seems quite explicit (emphasis mine):

Publishers may not attempt to discover the identity of a Google+ button user unless the user consents to share his or her identity with the Publisher via a Google-approved authorization procedure. This prohibition includes identifying users by correlating Google+ button reporting data from Google with Publisher data.

For the avoidance of doubt, this prohibition includes, but is not limited to, any use of pixels, cookies, or other methods to recognize users’ clicks on a Google+ button... Publishers may not direct users to click a Google+ button for purposes of misleading users...

I don't know what Google-approved authorization procedure is referred to in the first sentence.

Enforcement

I'm not sure how this will be accomplished, other than by web crawlers, but Google sounds like they are serious about it:

Google may analyze Publishers' use of a Google+ button to ensure Publishers’ compliance with these policies and to facilitate Google’s development of Google+ Buttons.

Google Analytics and Google Webmaster Tools

Yes, it is true that you can get aggregated Google +1 activity data on your own websites from Google Analytics. The same is true for Google Webmaster Tools, for your own site or others:

Google Webmaster Tools reports on all +1 interactions for your content, regardless of whether the interaction occurs on your own domain, or on a search result listing.

However, Google Webmaster Tools also aggregates reports on +1 activity related to your content, so no further detail can be determined.

Blogger and other social sharing

As @mvark mentioned, on a Blogger blog, if one is the owner, the admin panel displays how many +1's were given to each post (URL). Sometimes the person's identity is disclosed. That seems to be dependent on a variety of factors that include

• Designating that one's Google+ activity on non-Google and Google sites be publicly visible. This setting is in the user permissions page for one's own Google account; and
• Possibly if one has some form of Google+ circles relationship with another user who has +1'd that same URL. I have noticed this on non-Blogger websites as well.

EDIT

Here is a very recent page, from 29 October 2012, Google Developers, about Social Tracking. It has new information about Google+ tracking as well as Twitter and Facebook likes and un-likes. There is also a new Google+ private beta program, that might allow you to do what you requested, but I'm not sure who is eligible to participate in it.