The History API is currently in developer preview. Before trying to use it, make sure you have signed up. You may also want to go through the sample application to get an idea for what it does (and what it doesn't) doe and make sure it fits in with your needs. It is not an exact replacement for Facebook's solution.
If it does seem to meet your needs, you can probably use the PHP API at https://code.google.com/p/google-api-php-client/ to navigate the OAuth2 process, which is probably the trickiest part of the whole thing. You may also be able to use the Google+ Login button they have described as part of the History API. After that it is a matter of sending an insert command (via an HTTP POST documented at https://developers.google.com/+/history/#writing_moments) and making sure you have a page that has snippet markup information in it to be inserted (documented at https://developers.google.com/+/plugins/snippet and schema.org).