I guess this was a newbie question, but the answer really isn’t documented anywhere. So I looked through some of the Piwik code and figured it out. Here’s the solution in case other newbies need help with this.
The loggers are stored in the Zend Registry. To access them:
// All logs are written to dir "tmp/logs"
Zend_Registry::get('logger_message')->logEvent($errno, $errstr, $errfile, $errline, $backtrace);
By default, logs are displayed on-screen rather than written to file. To re-direct logging to the files, you’ll have to add the following lines to your config.ini.php file: