To accomplish that, you'll first need some JavaScript. As an example, have a look at this fiddle.

HTML:

<p>Users</p>
<ul id="users-list">
    <li><input type="text" name="names[]" value="" placeholder="enter name" /></li>
</ul>
<button id="add-more">Add More Users</button>

JS (using jQuery):

$(document).ready(function() {
    $users_list = $('#users-list');
    $add_more = $('#add-more');
    
    $add_more.on('click', function() {
        $users_list.find('li:first').clone().find(':input').val('').end().appendTo($users_list);
    });
});

Don't pay much attention to the actual code (it doesn't even include a form or a submit button, it's just a rough example); mostly focus on the logic so you can adapt it for your needs.

After you submit your form, the "names" input will be an array of strings instead of a single string (as it would be without the []).