1. To create a new module style for your Joomla! template, you need to add it to the bottom of the modules.php file that you just copied into your own template's directory:

/*
* Module style (chrome) that wraps the module in an unordered list
*/
function modChrome_ullist($module, &$params, &$attribs)
{
?>
<ul class="<?php echo $params->get('moduleclass_sfx'); ?>">
<?php if ($module->showtitle != 0) : ?>
<li class="title">
<?php echo $module->title; ?>
</li>
<?php endif; ?>
<li>
<?php echo $module->content; ?>
</li>
</ul>
<?php
}
?>

Note that you gave the function a relevant name (modChrome_ullist). This is good practice, as it makes it more obvious to anyone else working on your Joomla! template what you're trying to do!

2. If you now upload the modules.php file, your new module chrome will appear.

1. To see your new module chrome in the frontend of your Joomla! website, you need to open your template's index.php file (as you're using the rhuk_milkyway template, this is found in the \templates\rhuk_milkyway\ directory). Locate an instance of a jdoc statement in your template that makes use of the style attribute—a snippet of code that looks like this:

<jdoc:include
type="modules"
name="user1"
style="xhtml"
/>

2. You can change this to read:

<jdoc:include
type="modules"
name="user1"
style="ullist"
/>

3. Alternatively, you could add the following line, code style="ullist" into a jdoc statement if one doesn't already exist. If you now view the frontend of your website, you'll see a visual change to the user1 module:

4. There's also change behind the scenes in the HTML that is given. Previously, the HTML for this module looked like this:

<h3>Latest News</h3>
<ul class="latestnews">
<li class="latestnews">
<a href="(link omitted)" class="latestnews">Welcome to Joomla! </a>
</li>
<!-- other links omitted -->
</ul>

5. The new output HTML has changed structure:

<ul class="">
<li class="title">
Latest News
</li>
<li><ul class="latestnews">
<li class="latestnews">
<a href="(link omitted)" class="latestnews">Welcome to Joomla! </a>
</li>
<!-- other links omitted -->
</ul>
</li>
</ul>