This could be done in many different ways - even without editing any file. Install this extension: http://extensions.joomla.org/extension/advanced-module-manager and when editing module you'll have additional tab called "tasks" There will be field URL, type inside URLs of your registration form. Thanks to this you'll be able to assign modules to registration form.
You could also override for:
ROOT/components/com_community/templates/default/register.index.php
Copy it to:
ROOT/templates/your-template/html/com_community (if you don't have "html" or "com_community" folders, feel free to create them)
Then you may create module position inside file using this code:
$modules = JModuleHelper::getModules( 'reg-positon' );
foreach ($modules as $module) {
$_options = array( 'style' => 'xhtml' );
echo JModuleHelper::renderModule( $module, $_options );
}
Above code creates module position: "reg-positon'. You'll need to type this name manually as it will be not listed on module positions list.
Now you'll need a bit of html to display it on right or left of registration form.