How to go about combining dropdowns / filter queries?

To get you started: you can make a custom form (I never worked with wp_dropdown_categories). When the form is submitted, it gets the input variables and uses them in the query.

The form could be something like:

<form action="http://example.com/resultspage" method="post">
<select name="categories">
   <option value="categoryname1"></option>
   <option value="categoryname2"></option>
   <option value="categoryname3"></option>
</select>
<select name="tags">
   <option value="tagname1"></option>
   <option value="tagname2"></option>
   <option value="tagname3"></option>
</select>
<select name="authors">
   <option value="authorname1"></option>
   <option value="authorname2"></option>
   <option value="authorname3"></option>
</select>
<select name="archives">
   <option value="archivesname1"></option>
   <option value="archivesname2"></option>
   <option value="archivesname3"></option>
</select>
</form>

And then on the resultspage

$category = $_POST['categories'];
$tag = $_POST['tags'];
$author = $_POST['authors'];
$archive = $_POST['archives'];

$args = array(
    'category' => $category,
    'tag' => $tag,
    'author' => $author,
    'posts_per_page' => -1 // Number of posts per page, -1 is show all 
);

$query = new WP_Query($args);

A few notes. First, this is not tested. Second, check the codex on WP_Query how to use these (and other) arguments and what kind of input they need. For instance, you can use 'tag' and input the tag slug, but you can also use 'tag_id' and use the tag ID as input. Then you would change the option value of the tags select field. Third: I don’t know what you would like to do with the archives. Would you like to display posts from a certain month? This can be achieved with a meta_query (you can find documentation in the WP codex).

Is this a good start? Let me know if it worked out.