How to add some basic inline CSS using existing plugin or theme?

The easiest way to do this is using wp_add_inline_style … here is the documentation.

A great example I found on a public Gist:

<?php

//Adding CSS inline style to an existing CSS stylesheet
function wpb_add_inline_css() {

        //All the user input CSS settings as set in the plugin settings
        $slicknav_custom_css = "
            @media screen and (max-width: {$ng_slicknav_width}px) {
                {$ng_slicknav_menu} {
                  display: none;
               }
               .slicknav_menu {
                  display: block;
                  background: {$ng_slicknav_background};
               }
               .slicknav_btn {
                  background-color:{$ng_slicknav_button};
                  float:{$ng_slicknav_button_position};
               }
           }";

  //Add the above custom CSS via wp_add_inline_style
  wp_add_inline_style( 'slicknavcss', $slicknav_custom_css ); //Pass the variable into the main style sheet ID

}
add_action( 'wp_enqueue_scripts', 'wpb_add_inline_css' ); //Enqueue the CSS style

And if your plugin doesn’t have an existing stylesheet, you can register a “dummy” one like this:

wp_register_style( 'dummy-handle', false );
wp_enqueue_style( 'dummy-handle' );

wp_add_inline_style( 'dummy-handle', '* { color: red; }' );