in forum you can set in profile. some forum or blog recognize by email address, you can set avatar from this site https://en.gravatar.com/
There you will see the option of Edit picture or Edit avatar it will help you to select the right image and avatar. This job is almost same in all kinds of forum like phpbb, vbulletin, punbb, mybb, SMF and so on.
To have your photo appear in the Google search result pages when ever your blogs appear in search results, You must enable Google authorship markup on your site. See how you can do it here in the google help - https://plus.google.com/authorship . Also look at this http://www.google.com/insidesearch/features/authorship/index.html . These are also called as rich snippets by Google.