You need to add your css to wp_head. In order to do so, you need to get your dynamic CSS first, load in into a variable and then add that variable to the head output. Just like so:
(This code can go into your functions.php, plugin file or somewhere else in your theme, make sure you include this code in a file where it can be called properly)
<?php
function so_output_dynamic_css() {
// do some stuff to get your CSS here..
$some_dynamic_css = "body {background: green;}";
?>
<style type="text/css" id="so-dynamic-css">
<?php echo $some_dynamic_css; ?>
</style>
<?php }
add_action('wp_head', 'so_output_dynamic_css');