Not so easy at the moment, I'm afraid. There would be 3 stages involved:
1. You can retrieve the most popular tags as part of a page's access to the database by modifying the qa_db_select_with_pending(...) function on the appropriate page to use qa_db_popular_tags_selectspec(0). For example on the questions page, you could change this in qa-page-home.php:
list($questions, $count)=qa_db_select_with_pending($qa_db,
qa_db_recent_qs_selectspec($qa_login_userid, $qa_start),
qa_db_options_cache_selectspec('cache_qcount')
);
...to...
list($questions, $count, $populartags)=qa_db_select_with_pending($qa_db,
qa_db_recent_qs_selectspec($qa_login_userid, $qa_start),
qa_db_options_cache_selectspec('cache_qcount'),
qa_db_popular_tags_selectspec(0)
);
2. Lower down on the same page, after qa_content_prepare(), add the $populartags variable to $qa_content, perhaps as follows:
$qa_content['populartags']=$populartags;
3. Create a custom theme (see Advanced page on main site) and override the sidebar() function to do something with $this->content['populartags']. To start with you can print_r it, just to get an idea of what it contains. You can use qa_tag_html() to convert a tag to the standard HTML representation.
Good luck and let us know how it goes!